Results 251 to 260 of about 70,095 (287)

Required scientific floating point arithmetic

1978 IEEE 4th Symposium onomputer Arithmetic (ARITH), 1978
Previous papers in computer arithmetic have shown that correct rounded floating point with good arithmetic properties can be attained using guard digits and careful algorithms on the floating point fractions. This paper combines that body of knowledge with proposed exponent forms that are closed with respect to inversion and detection and recovery of ...
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On Local Roundoff Errors in Floating-Point Arithmetic

Journal of the ACM, 1973
A bound on the relative error in floating-point addition using a single-precision accumulator with guard digits is derived. It is shown that even with a single guard digit, the accuracy can be almost as good as that using a double-precision accumulator.
Toyohisa Kaneko, Bede Liu
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An IEEE floating point arithmetic implementation

1983 IEEE 6th Symposium on Computer Arithmetic (ARITH), 1983
This article describes some of the methods and algorithms used in an implementation of floating point arithmetic following (almost) the IEEE standard defined in (1). The description is more directly algorithm-oriented than the ‘Implementation Guide’ for this standard (2), since the latter does not treat an actual implementation.
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Unum: Adaptive Floating-Point Arithmetic

2016 Euromicro Conference on Digital System Design (DSD), 2016
Usually, arithmetic units represent numeric data-types employing fixed-length representations. For instance, hardware representations of real numbers usually employ fixed-length formats defined by the IEEE Standard 754 (32-bit single-precision, 64-bit double-precision, , floating-point numbers).
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Analysis of Rounding Methods in Floating-Point Arithmetic

IEEE Transactions on Computers, 1977
The error properties of floating-point arithmetic using various rounding methods (including ROM rounding, a new scheme) are analyzed. Guard digits are explained, and the rounding schemes' effectiveness are evaluated and compared.
David J. Kuck, Douglas Stott Parker Jr., Ahmed H. Sameh   +2 more
exaly   +3 more sources

Formalization and implementation of floating-point arithmetics

Computing, 1975
The paper is intended to show that floating-point arithmetic can be implemented in a way which leads to reasonable mathematical structures as described in chapters 5 and 6. It turns out for instance that all the rules of the minus-operator of the real numbers can be saved and that with respect to ≦ and ≧ inequalities can be manipulated as if they were ...
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Floating-Point Arithmetic

2019
You already know about integer arithmetic; now we will introduce some floating-point computations. There is nothing difficult here; a floating-point value has a decimal point in it and zero or more decimals. We have two kinds of floating-point numbers: single precision and double precision.
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Floating point arithmetic and digital filters

IEEE Transactions on Signal Processing, 1992
The roundoff noise properties of floating point digital filters are examined. To make the analysis tractable, a high level model to deal with the errors in the inner product operation is developed. This model establishes a broad connection between coefficient sensitivity and roundoff noise.
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Is Floating-Point. Arithmetic Still Adequate?

1988
For complicated numerical problems, the error analysis has to be performed by the computer. Several methods for automated error analysis are known. Floating-point arithmetic has to be augmented and programming languages for scientific computation have to be provided (PASCAL-SC and FORTRAN-SC) for that purpose.
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Accurate and Reliable Computing in Floating-Point Arithmetic

2010
Methods will be discussed on how to compute accurate and reliable results in pure floating-point arithmetic. In particular, verification methods with INTLAB and error-free transformations will be presented in some detail.
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