Results 231 to 240 of about 4,893,936 (283)
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2020
Working with big integers can be seen as an abstract art, and if the cryptosystems are not implemented properly, the entire cryptographic algorithm or scheme can lead to a real disaster. This chapter focuses on floating-point arithmetic and its importance for cryptography.
Marius Iulian Mihailescu +1 more
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Working with big integers can be seen as an abstract art, and if the cryptosystems are not implemented properly, the entire cryptographic algorithm or scheme can lead to a real disaster. This chapter focuses on floating-point arithmetic and its importance for cryptography.
Marius Iulian Mihailescu +1 more
+4 more sources
An Automatable Formal Semantics for IEEE-754 Floating-Point Arithmetic
, 2015 Automated reasoning tools often provide little or no support to reason accurately and efficiently about floating-point arithmetic. As a consequence, software verification systems that use these tools are unable to reason reliably about programs ...
Cesare Tinelli +2 more
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Unnormalized Floating Point Arithmetic
Journal of the ACM, 1959Algorithms for floating point computer arithmetic are described, in which fractional parts are not subject to the usual normalization convention. These algorithms give results in a form which furnishes some indication of their degree of precision. An analysis of one-stage error propagation is developed for each operation; a suggested statistical model ...
Robert L. Ashenhurst +1 more
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Floating point arithmetic on a RISC
Microprocessing and Microprogramming, 1988Abstract A set of high-speed floating point procedures for the newly proposed microcoded RISC system is presented. Their performance is compared to that of other RISC-type systems, to other microprocessors as well as mainframes. The performance is found to be competitive and in some cases--exceeding that of other systems.
Jean M. Davila +2 more
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A Hierarchical Block-Floating-Point Arithmetic
Journal of VLSI signal processing systems for signal, image and video technology, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shiro Kobayashi, Gerhard P. Fettweis
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Journal of the ACM, 1960
Three types of floating-point arithmetics with error control are discussed and compared with conventional floating-point arithmetic. General multiplication and division shift criteria are derived (for any base) for Metropolis-type arithmetics. The limitations and most suitable range of application for each arithmetic are discussed.
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Three types of floating-point arithmetics with error control are discussed and compared with conventional floating-point arithmetic. General multiplication and division shift criteria are derived (for any base) for Metropolis-type arithmetics. The limitations and most suitable range of application for each arithmetic are discussed.
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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 ...
Daniel Kroening, Thomas Wahl
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Roundings in floating point arithmetic
1972 IEEE 2nd Symposium on Computer Arithmetic (ARITH), 1972In this paper we discuss directed roundings and indicate how hardware might be designed to produce proper upward-directed, downward-directed, and certain commonly used symmetric roundings. Algorithms for the four binary arithmetic operations and for rounding are presented, together with proofs of their correctness; appropriate formulas for a priori ...
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Arithmetic Coding for Floating-Point Numbers
2021 IEEE Conference on Dependable and Secure Computing (DSC), 2021To enable the usage of standard hardware in safety-critical applications for production systems, new approaches for hardware fault tolerance are required. These approaches must be implemented on software level. As shown in the literature, arithmetic coding is a promising approach, but only supports integer calculations.
Marc Fischer +3 more
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Axiomatizations of floating point arithmetics
1985 IEEE 7th Symposium on Computer Arithmetic (ARITH), 1985We present a universal scheme for axiomatizing floating point ariththmetic. The schema can be used to axiomatize any floating point arithmetic. It consists of a labeled graph with vertices describing some arithmetical properties and edges containing appropriate axioms. The language of floating point arithmetic is developed gradually in this scheme. The
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