Results 11 to 20 of about 3,501 (259)
Acta Numerica, 2023 Floating-point numbers have an intuitive meaning when it comes to physics-based numerical computations, and they have thus become the most common way of approximating real numbers in computers. The IEEE-754 Standard has played a large part in making floating-point arithmetic ubiquitous today, by specifying its semantics in a strict yet useful way as ...
Boldo, Sylvie +3 more
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Hammering Floating-Point Arithmetic
, 2023 AbstractSledgehammer, a component of the interactive proof assistant Isabelle/HOL, aims to increase proof automation by automatically discharging proof goals with the help of external provers. Among these provers are a group of satisfiability modulo theories (SMT) solvers with support for the SMT-LIB input language.
Olle Torstensson, Tjark Weber
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Quantum Circuits for Floating-Point Arithmetic [PDF]
, 2018 Quantum algorithms to solve practical problems in quantum chemistry, materials science, and matrix inversion often involve a significant amount of arithmetic operations which act on a superposition of inputs. These have to be compiled to a set of fault-tolerant low-level operations and throughout this translation process, the compiler aims to come ...
Thomas Häner +3 more
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Detecting Floating-Point Expression Errors Based Improved PSO Algorithm
IET Software, 2023 The use of floating-point numbers inevitably leads to inaccurate results and, in certain cases, significant program failures. Detecting floating-point errors is critical to ensuring that floating-point programs outputs are proper.
Hongru Yang +4 more
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Journal of Advances in Modeling Earth Systems, 2020 The need for high‐precision calculations with 64‐bit or 32‐bit floating‐point arithmetic for weather and climate models is questioned. Lower‐precision numbers can accelerate simulations and are increasingly supported by modern computing hardware.
M. Klöwer, P. D. Düben, T. N. Palmer
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FAST ROBUST ARITHMETICS FOR GEOMETRIC ALGORITHMS AND APPLICATIONS TO GIS [PDF]
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2021 Geometric predicates are used in many GIS algorithms, such as the construction of Delaunay Triangulations for Triangulated Irregular Networks (TIN) or geospatial predicates.
T. Bartels, V. Fisikopoulos
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Mixed abstractions for floating-point arithmetic [PDF]
2009 Formal Methods in Computer-Aided Design, 2009 Floating-point arithmetic is essential for many embedded and safety-critical systems, such as in the avionics industry. Inaccuracies in floating-point calculations can cause subtle changes of the control flow, potentially leading to disastrous errors. In this paper, we present a simple and general, yet powerful framework for building abstractions from ...
Angelo Brillout +2 more
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Robustness Analysis of Floating-Point Programs by Self-Composition
Journal of Applied Mathematics, 2014 Robustness is a key property for critical systems that run in uncertain environments, to ensure that small input perturbations can cause only small output changes.
Liqian Chen +4 more
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High-Performance Computation in Residue Number System Using Floating-Point Arithmetic
Computation, 2021 Residue number system (RNS) is known for its parallel arithmetic and has been used in recent decades in various important applications, from digital signal processing and deep neural networks to cryptography and high-precision computation.
Konstantin Isupov
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Interval Term Rewriting System: Toward A Formal Model for Interval Computation
Trends in Computational and Applied Mathematics, 2006 We present a term rewriting system for interval arithmetic (addition, subtraction and multiplication), toward a mathematical model for interval compu- tation.
A.X. Carvalho, R.H.N. Santiago
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