# Mathematical Foundation of Computer Arithmetic

@article{Kulisch1977MathematicalFO, title={Mathematical Foundation of Computer Arithmetic}, author={Ulrich W. Kulisch}, journal={IEEE Transactions on Computers}, year={1977}, volume={C-26}, pages={610-621} }

During recent years a number of papers concerning a mathematical foundation of computer arithmetic have been written. Some of these papers are still unpublished. The papers consider the spaces which occur in numerical computations on computers depending on a properly defined computer arithmetic. The following treatment gives a summary of the main ideas of these papers. Many of the proofs had to be sketched or completely omitted. In such cases the full information can be found in the references.

## 5 Citations

### A Survey of Some Recent Contributions to Computer Arithmetic

- Computer ScienceIEEE Transactions on Computers
- 1976

This paper surveys some recent contributions to computer arithmetic. The survey includes floating-point arithmetic, nonstandard number systems, and the generation of elementary functions. The design…

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### Error analysis of linear recursions in floating point

- MathematicsICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing
- 1985

A stochastic error model for floating point arithmetic is developed and used to study the effects of finite wordlength on linear recursive formulas. Optimal realizations exist, but they are highly…

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Abstract : The report is the first one of a series of three papers which are intended to given an axiomatic approach to those spaces in which numerical computations are usually done. The first part…

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- Mathematics
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The present paper is intended to give an axiomatic approach to rounded computations. A rounding is defined as a monotone mapping of an ordered set into a subset, which in general is called a lower…

### Roundings in floating point arithmetic

- Computer ScienceIEEE Symposium on Computer Arithmetic
- 1972

In this paper, algorithms for the four binary arithmetic operations and for rounding are presented, together with proofs of their correctness; appropriate formulas for a priori error analysis of these algorithms are presented.

### Floating-Point Computation of Functions with Maximum Accuracy

- MathematicsIEEE Transactions on Computers
- 1977

Algorithms are given that compute multiple sums and products and arbitrary roots of floating-point numbers with maximum accuracy, The summation algorithm can be applied to compute scalar products,…

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It is shown that the concept of a screen is equivalent to the idea of a certain sublattice and using this relation further necessary and sufficient conditons for a screen can be derived from lattice theory.

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The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.

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In an aircraft having a pair of engines mounted forwardly of the wing and discharging jet exhaust over the wing for augmented lift, a trailing edge flap is positioned directly behind each of the engines to generate vortices in the jet exhaust that travels over the upper surfaces of the flaps.

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Durch maschinenorientierte Operatoren wird eine Maschinenintervallarithmetik beschrieben und gezeigt, daß bereits ein Teil dieser operatoren zur Realisierung der Intervallarechnung erzeugen, die ein bestimmtes Rundungsverhalten aufweist.

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