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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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14 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2017

Automatic Estimation of Verified Floating-Point Round-Off Errors via Static Analysis

This paper introduces a static analysis technique for computing formally verified round-off error bounds of floating-point functional expressions. The technique is based on a denotational semantics that computes a symbolic estimation of floating-point round-o errors along with a proof certificate that ensures its correctness. The symbolic estimation can be evaluated on concrete inputs using rigorous enclosure methods to produce formally verified numerical error bounds. The proposed technique is implemented in the prototype research tool PRECiSA (Program Round-o Error Certifier via Static Analysis) and used in the verification of floating-point programs of interest to NASA.

Moscato, Mariano↗
NASA NTRS2018

An Abstract Interpretation Framework for the Round-Off Error Analysis of Floating-Point Programs

This paper presents an abstract interpretation framework for the round-off error analysis of floating-point programs. This framework defines a parametric abstract analysis that computes, for each combination of ideal and floating-point execution path of the program, a sound over-approximation of the accumulated floating-point round-off error that may occur. In addition, a Boolean expression that characterizes the input values leading to the computed error approximation is also computed. An abstraction on the control flow of the program is proposed to mitigate the explosion of the number of elements generated by the analysis. Additionally, a widening operator is defined to ensure the convergence of recursive functions and loops. An instantiation of this framework is implemented in the prototype tool PRECiSA that generates formal proof certificates stating the correctness of the computed round-off errors.

Titolo, Laura↗
NASA NTRSDate not supplied

PRECiSA: a static analysis tool for floating-point programs

This presentation introduces PRECiSA, a static analysis framework for analyzing floating-point programs. PRECiSA computes round-off error bounds for a class of floating-point programs, and produces a formal proof certificate of the correctness of these bounds. PRECiSA also has the capability of generating C code which is instrumented to detect unstable branching conditions from a real-number algorithm specification.

Floating-point↗
NASA NTRSDate not supplied

Automatic Generation of Guard-Stable Floating-Point Code

In floating-point programs, test instability occurs when the control flow of a conditional statement diverges from its ideal execution under real arithmetic. This phenomenon is caused by the presence of round-off errors in floating-point computations. Writing programs that correctly handle test instability often require expertise on finite precision computations and rounding errors. This paper presents a fully automatic tool chain that generates and formally verifies a test-stable floating-point C program from its functional specification in real arithmetic. The generated program is instrumented to soundly detect when unstable tests may occur and, in these cases, to issue a warning. The proposed approach combines the PRECiSA floating-point static analyzer, the Frama-C software verification suite, and the PVS theorem prover.

Floating-Point Arithmetic↗
NASA NTRS1990

Verification of floating-point software

Floating point computation presents a number of problems for formal verification. Should one treat the actual details of floating point operations, or accept them as imprecisely defined, or should one ignore round-off error altogether and behave as if floating point operations are perfectly accurate. There is the further problem that a numerical algorithm usually only approximately computes some mathematical function, and we often do not know just how good the approximation is, even in the absence of round-off error. ORA has developed a theory of asymptotic correctness which allows one to verify floating point software with a minimum entanglement in these problems. This theory and its implementation in the Ariel C verification system are described. The theory is illustrated using a simple program which finds a zero of a given function by bisection. This paper is presented in viewgraph form.

Hoover, Doug N.↗
NASA NTRS2019

A Mixed Real and Floating-Point Solver

Reasoning about mixed real and floating-point constraints is essential for developing accurate analysis tools for floating-point pro- grams. This paper presents FPRoCK, a prototype tool for solving mixed real and floating-point formulas. FPRoCK transforms a mixed formula into an equisatisfiable one over the reals. This formula is then solved using an off-the-shelf SMT solver. FPRoCK is also integrated with the PRECiSA static analyzer, which computes a sound estimation of the round-off error of a floating-point program. It is used to detect infeasible computational paths, thereby improving the accuracy of PRECiSA.

Salvia, Rocco↗
NASA NTRSDate not supplied

A Provably Correct Floating-Point Implementation of Well Clear Avionics Concepts

The NASA DAIDALUS library provides formal definitions for Detect-and-Avoid avionics concepts such as when an aircraft is well-clear with respect to the surrounding air traffic, i.e., it does not operate in such proximity to create a collision hazard. While several properties are proven correct for DAIDALUS assuming ideal real number arithmetic, an actual implementation that uses floating-point numbers may behave unexpectedly because of round-off errors and run-time exceptions. This paper presents an experience report on the application of a formal methods toolchain to extract and verify floating-point C code from a real-valued specification of the well-clear module of DAIDALUS. This toolchain comprises the PVS theorem prover, the PRECiSA floating-point analyzer and code generator, and the Frama-C analysis suite. The generated code is automatically instrumented to detect when the control flow of the floating-point program may diverge from the ideal real number specification, and it is annotated with contracts that state the maximum accumulated round-off error. The absence of overflows is also formally verified for the generated code. In order to apply the toolchain to an industrial case study such as DAIDALUS, a formally verified pre-processing of the input specification is performed, which includes a program slicing and several semantic-preserving simplifications.

Program verification↗
NASA NTRS2000

A Very High Order, Adaptable MESA Implementation for Aeroacoustic Computations

Since computational efficiency and wave resolution scale with accuracy, the ideal would be infinitely high accuracy for problems with widely varying wavelength scales. Currently, many of the computational aeroacoustics methods are limited to 4th order accurate Runge-Kutta methods in time which limits their resolution and efficiency. However, a new procedure for implementing the Modified Expansion Solution Approximation (MESA) schemes, based upon Hermitian divided differences, is presented which extends the effective accuracy of the MESA schemes to 57th order in space and time when using 128 bit floating point precision. This new approach has the advantages of reducing round-off error, being easy to program. and is more computationally efficient when compared to previous approaches. Its accuracy is limited only by the floating point hardware. The advantages of this new approach are demonstrated by solving the linearized Euler equations in an open bi-periodic domain. A 500th order MESA scheme can now be created in seconds, making these schemes ideally suited for the next generation of high performance 256-bit (double quadruple) or higher precision computers. This ease of creation makes it possible to adapt the algorithm to the mesh in time instead of its converse: this is ideal for resolving varying wavelength scales which occur in noise generation simulations. And finally, the sources of round-off error which effect the very high order methods are examined and remedies provided that effectively increase the accuracy of the MESA schemes while using current computer technology.

Dydson, Roger W.↗
NASA NTRS2019

Provably Correct Floating-Point Implementation of a Point-In-Polygon Algorithm

The problem of determining whether or not a point lies inside a given polygon occurs in many applications. In air traffic management concepts, a correct solution to the point-in-polygon problem is critical to geofencing systems for Unmanned Aerial Vehicles and in weather avoidance applications. Many mathematical methods can be used to solve the point-in-polygon problem. Unfortunately, a straightforward floating- point implementation of these methods can lead to incorrect results due to round-off errors. In particular, these errors may cause the control flow of the program to diverge with respect to the ideal real-number algorithm. This divergence potentially results in an incorrect point-in- polygon determination even when the point is far from the edges of the polygon. This paper presents a provably correct implementation of a point-in-polygon method that is based on the computation of the winding number. This implementation is mechanically generated from a source- to-source transformation of the ideal real-number specification of the algorithm. The correctness of this implementation is formally verified within the Frama-C analyzer, where the proof obligations are discharged using the Prototype Verification System (PVS).

Moscato, Mariano M.↗