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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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Floating-point arithmetic in the Coq system
Information and Computation, 2012 Floating point arithmetic is not only an important aspect of computation but has also become an important aspect of proofs. Hales' proof of the Kepler conjecture is probably the most famous of such proofs. If these proofs are to be trusted then it is necessary to rely on the correctness of the computations.
Guillaume Melquiond
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Optimal Architecture of Floating-Point Arithmetic for Neural Network Training Processors [PDF]
Sensors, 2022 The convergence of artificial intelligence (AI) is one of the critical technologies in the recent fourth industrial revolution. The AIoT (Artificial Intelligence Internet of Things) is expected to be a solution that aids rapid and secure data processing.
Muhammad Junaid +3 more
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Simulating Low Precision Floating-Point Arithmetic [PDF]
SIAM Journal of Scientific Computing, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nicholas J Higham, Srikara Pranesh
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Efficient Floating Point Arithmetic for Quantum Computers
IEEE Access, 2022 One of the major promises of quantum computing is the realization of SIMD (single instruction - multiple data) operations using the phenomenon of superposition.
Raphael Seidel +4 more
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Floating Point Optimization Using VHDL [PDF]
Engineering and Technology Journal, 2009 Due to inherent limitations of the fixed-point representation, it is sometimes desirable to perform arithmetic operations in the floating-point format.
Manal Hammadi Jassim
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Mathematics, 2021 The aim of this paper is to present a new method and the tool to validate the numerical results of the Volterra integral equation with discontinuous kernels in linear and non-linear forms obtained from the Adomian decomposition method.
Samad Noeiaghdam +4 more
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An Imprecise but Infinite Fall: The Machine Performance of Floating-Point Arithmetic
Proceedings, 2021 Floating-point arithmetic is a common computational method, used to represent large or infinite space in software, such as game engines. This paper explores floating-point arithmetic in the game engine Unity, as it renders an infinitely falling object ...
Kelsey Brod
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Multi‐precision binary multiplier architecture for multi‐precision floating‐point multiplication
IET Circuits, Devices and Systems, 2021 Arithmetic logic units (ALUs) are core components of processing devices that perform required arithmetic and logical operations such as multiplication, division, addition, subtraction, and squaring. The multiplication operation is frequently used in ALUs
Geetam Singh Tomar +2 more
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Exact Versus Inexact Decimal Floating-Point Numbers and Arithmetic
IEEE Access, 2023 The IEEE 754 standard does not distinguish between exact and inexact floating-point numbers. There is no bit or field in the binary encoding that indicates whether a floating-point number is exact or not.
Muhamed F. Mudawar
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