Results 281 to 290 of about 205,230 (331)

Tapered Floating Point: A New Floating-Point Representation

IEEE Transactions on Computers, 1971
It is well known that there is a possible tradeoff in the binary representation of floating-point numbers in which one bit of accuracy can be gained at the cost of halving the exponent range, and vice versa. A way in which the exponent range can be greatly increased while preserving full accuracy for most computations is suggested.
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On accurate floating-point summation

Communications of the ACM, 1971
cumulation 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

The NS32081 Floating-point Unit

IEEE Micro, 1986
This 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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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), 2018
This 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, Volodymyr Samotyy, Oleh Horyachyy   +2 more
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Roundings in floating point arithmetic

1972 IEEE 2nd Symposium on Computer Arithmetic (ARITH), 1972
In 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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Unnormalized Floating Point Arithmetic

Journal of the ACM, 1959
Algorithms 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, Nicholas C. Metropolis   +1 more
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Floating-Point Arithmetics

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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Multiprecision floating point addition

Proceedings of the 2000 international symposium on Symbolic and algebraic computation, 2000
An 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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Iterative Refinement in Floating Point

Journal of the ACM, 1967
Iterative 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.
openaire   +3 more sources

Accurate floating-point summation

Communications of the ACM, 1970
This paper describes an alternate method for summing a set of floating-point numbers. Comparison of the error bound for this method with that of the standard summation method shows that it is considerably less sensitive to propagation of round-off error.
exaly   +2 more sources