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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Handbook of Floating-Point Arithmetic [PDF]
, 2010 International audienceThis handbook is a definitive guide to the effective use of modern floating-point arithmetic. Floating-point arithmetic has considerably evolved, from the frequently inconsistent floating-point number systems of early computing to ...
Muller, Jean-Michel +8 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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Maximum network flow with floating point arithmetic [PDF]
Information Processing Letters, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Althaus, E., Mehlhorn, K.
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Trans-floating-point arithmetic removes nine quadrillion redundancies from 64-bit IEEE 754 floating-point arithmetic [PDF]
, 2014 IEEE 754 floating-point arithmetic is widely used in modern, general-purpose computers. It is based on real arithmetic and is made total by adding both a positive and a negative infinity, a negative zero, and many Not-a-Number (NaN) states.
Anderson, James A.D.W.
core +6 more sources
A unified closed-loop stability measure for finite-precision digital controller realizations implemented in different representation schemes [PDF]
, 2003 A computationally tractable unified finite word length closed-loop stability measure is derived which is applicable to fixed-point, floating-point and block- floating-point representation schemes.
Whidborne, James F. +7 more
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Optimal Realizations of Floating-Point Implemented Digital Controllers with Finite Word Length Considerations [PDF]
, 2004 The closed-loop stability issue of finite-precision realizations is investigated for digital controllers implemented in floating-point arithmetic.
Chu, J. +3 more
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Optimal Controller and Filter Realisations using Finite-precision, Floating- point Arithmetic. [PDF]
, 2005 The problem of reducing the fragility of digital controllers and filters implemented using finite-precision, floating-point arithmetic is considered.
Whidborne, James F. +7 more
core +1 more source
Design and Implementation of POSIT Based Adder and Multiplier in Verilog HDL [PDF]
E3S Web of Conferences, 2023 Due to recent developments, the POSIT number system, winch has been planned as a successor for numbers that are expressed in IEEE floating-point, which are in the focus of advances in arithmetic.
Sanivarapu Rambabu +5 more
doaj +1 more source
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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