Results 1 to 10 of about 304 (113)
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 ...
Daniel Kroening, Thomas Wahl
exaly +2 more sources
Simulating Low Precision Floating-Point Arithmetic [PDF]
SIAM Journal of Scientific Computing, 2019 The half-precision (fp16) floating-point format, defined in the 2008 revision of the IEEE standard for floating-point arithmetic, and a more recently proposed half-precision format bfloat16, are increasingly available in GPUs and other accelerators.
Nicholas Higham, Srikara Pranesh
exaly +4 more sources
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
openaire +3 more sources
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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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Design and Implementation of Numerical Linear Algebra Algorithms on Fixed Point DSPs
EURASIP Journal on Advances in Signal Processing, 2007 Numerical linear algebra algorithms use the inherent elegance of matrix formulations and are usually implemented using C/C++ floating point representation.
Nguyen Ha Thai +2 more
doaj +2 more sources