Results 211 to 220 of about 97,714 (259)
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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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On accurate floating-point summation
Communications of the ACM, 1971cumulation of floating-point sums is considered on a computer which performs t -digit base β floating-point addition with exponents in the range — m to M .
exaly +3 more sources
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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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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On Floating‐Point Normal Vectors
Computer Graphics Forum, 2010AbstractIn 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 250.2 uniformly distributed normals ...
Quirin Meyer +4 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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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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Multiprecision floating point addition
Proceedings of the 2000 international symposium on Symbolic and algebraic computation, 2000An efficient algorithm is presented that returns the exactly rounded sum of two multiprecision floating point numbers. Depending on the input signs and exponents the algorithm distinguishes five cases. In each case, the method minimizes the number of computer words that are subject to de-normalization, addition or subtraction, and normalization.
George E. Collins, Werner Krandick
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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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The NS32081 Floating-point Unit
IEEE Micro, 1986This chip's designers kept the hardware relatively simple and yet obtained high, IEEE-standard, floating-point performance.
Moshe Oavrielov, Lev Epstein
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