Results 231 to 240 of about 641,208 (284)

The Accuracy of Floating Point Summation

SIAM Journal of Scientific Computing, 1993
The author studies five summation methods for computing the sum of a number of floating point numbers. The accuracy is compared using rounding error analysis and numerical experiments. Reordering the numbers is a central idea. Statistical estimates are provided and the model with no guard digit is also considered. No particular method is uniformly more
Nicholas J Higham
exaly   +4 more sources

Floating-Point Tricks

IEEE Computer Graphics and Applications, 1997
The author discusses IEEE floating point representation that stores numbers in what amounts to scientific notation. He considers the sign bit, the logarithm function, function approximations, errors and refinements.
Gerben J. Hekstra, Ed F. Deprettere
openaire   +2 more sources

Beyond Floating Point

Journal of the ACM, 1984
A new number system is proposed for computer arithmetic based on iterated exponential functions. The main advantage is to eradicate overflow and underflow, but there are several other advantages and these are described and discussed.
C. W. Clenshaw, Frank W. J. Olver
openaire   +1 more source

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.
openaire   +2 more sources

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
openaire   +1 more source

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 ...
openaire   +1 more source

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
openaire   +1 more source

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.
openaire   +1 more source

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
openaire   +2 more sources