In numerical analysis, one or more guard digits can be used to reduce the amount of roundoff error. For example, suppose that the final result of a… (More)

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2006

2006

- Peter Kornerup, Jean-Michel Muller
- IEEE Transactions on Computers
- 2006

Redundant number representations are generally used to allow constant time additions, based on the fact that only bounded carry… (More)

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1989

1989

- Charles B. Dunham
- SGNM
- 1989

Under favourable conditions, evaluation of polynomials by Homer's rule has an error not exceeding a few units in the last place… (More)

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1985

1985

- Richard Goodman, Alan Feldstein, Joaquín Bustoz
- Computing
- 1985

A model of the relative error in floating point multiplication is developed and is analyzed stochastically for various choices of… (More)

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1984

1984

- Cliff B. Jones
- ACM Trans. Math. Softw.
- 1984

Multiple-precision arithmetic overcomes the round-off error incurred in conventional floating-point arithmetic, at the cost of… (More)

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1978

1978

- Lawrence A. Liddiard
- 1978 IEEE 4th Symposium onomputer Arithmetic…
- 1978

Previous papers in computer arithmetic have shown that correct rounded floating point with good arithmetic properties can be… (More)

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1977

1977

- Richard Goodman, Alan Feldstein
- Computing
- 1977

The effect of two important computer design parameters on floating point multiplication is studied. The parameters are the number… (More)

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1975

1975

- David J. Kuck, Douglas Stott Parker, Ahmed H. Sameh
- 1975 IEEE 3rd Symposium on Computer Arithmetic…
- 1975

ROM-rounding is introduced and is shown to compare favorably with existing floating-point rounding methods on design… (More)

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1974

1974

- William Kahan
- ACM Annual Conference
- 1974

Solving a linear system Ax = b by Gaussian Elimination usually entails pivotal inter-changes designed to inhibit that explosive… (More)

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1973

1973

- Toyohisa Kaneko, Bede Liu
- J. ACM
- 1973

A bound on the relative error in floating-point addition using a single-precision accumulator with guard digits is derived. It is… (More)

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1973

1973

- H. Kuki, W. J. Cody
- Commun. ACM
- 1973

This paper presents the statistical results of tests of the accuracy of certain arithmetic systems in evaluating sums, products… (More)

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