Results 231 to 240 of about 4,958,187 (282)
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The Accuracy of Floating Point Summation
SIAM Journal of Scientific Computing, 1993The usual recursive summation technique is just one of several ways of computing the sum of n floating point numbers. Five summation methods and their variations are analyzed here. The accuracy of the methods is compared using rounding error analysis and numerical experiments.
Nicholas Higham
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An Effective Floating-Point Reciprocal
2018 IEEE 4th International Symposium on Wireless Systems within the International Conferences on Intelligent Data Acquisition and Advanced Computing Systems (IDAACS-SWS), 2018This paper describes a simple and accurate floating-point reciprocal algorithm based on two modified Newton-Raphson iterations with a magic constant as the initial approximation. It can be effectively implemented on platforms with no FPU support since it uses just addition, multiplication and fused multiply-add operations.
Leonid V. Moroz +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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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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What Every Computer Scientist Should Know About Floating-Point Arithmetic
ACM Computing Surveys, 1991 Floating-point arithmetic is considered an esotoric subject by many people. This is rather surprising, because floating-point is ubiquitous in computer systems: Almost every language has a floating-point datatype; computers from PCs to supercomputers ...
David M. Goldberg
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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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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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Iterative Refinement in Floating Point
Journal of the ACM, 1967Iterative refinement reduces the roundoff errors in the computed solution to a system of linear equations. Only one step requires higher precision arithmetic. If sufficiently high precision is used, the final result is shown to be very accurate.
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A floating point unit for the 68040
Proceedings., 1990 IEEE International Conference on Computer Design: VLSI in Computers and Processors, 2002The Motorola 68040 floating point unit (FPU) combines three independent state machines, two data paths, and over 100000 transistors to achieve 8-Mflops peak performance and over 3-Mflops Linpack double-precision performance at the introductory speed of 25 MHz.
Shawn McCloud +6 more
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On Floating‐Point Normal Vectors
Computer Graphics Forum, 2010Abstract In this paper we analyze normal vector representations. We derive the error of the most widely used representation, namely 3D floating‐point normal vectors. Based on this analysis, we show that, in theory, the discretization error inherent to single precision floating‐point normals can be achieved by
Quirin Meyer +4 more
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