THE IEEE STANDARDS COMMITTEE P1788 FOR INTERVAL ARITHMETIC REQUIRES AN EXACT DOT PRODUCT

Ulrich Kulisch

2010

Abstract

Computing with guarantees is based on two arithmetical features. One is fixed (double) precision interval arithmetic. The other one is dynamic precision interval arithmetic, here also called long interval arithmetic. The basic tool to achieve high speed dynamic precision arithmetic for real and interval data is an exact multiply and accumulate operation and with it an exact dot product. Actually the simplest and fastest way for computing a dot product is to compute it exactly. Pipelining allows to compute it at the same high speed as vector operations on conventional vector processors. Long interval arithmetic fully benefits from such high speed. Exactitude brings very high accuracy, and thereby stability into computation. This document is intended to provide some background information, to increase the awareness, and to informally specify the implementation of an exact dot product.

References

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Paper Citation


in Harvard Style

Kulisch U. (2010). THE IEEE STANDARDS COMMITTEE P1788 FOR INTERVAL ARITHMETIC REQUIRES AN EXACT DOT PRODUCT . In Proceedings of the 12th International Conference on Enterprise Information Systems - Volume 3: ICEIS, ISBN 978-989-8425-06-5, pages 475-478. DOI: 10.5220/0002906204750478


in Bibtex Style

@conference{iceis10,
author={Ulrich Kulisch},
title={THE IEEE STANDARDS COMMITTEE P1788 FOR INTERVAL ARITHMETIC REQUIRES AN EXACT DOT PRODUCT},
booktitle={Proceedings of the 12th International Conference on Enterprise Information Systems - Volume 3: ICEIS,},
year={2010},
pages={475-478},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002906204750478},
isbn={978-989-8425-06-5},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 12th International Conference on Enterprise Information Systems - Volume 3: ICEIS,
TI - THE IEEE STANDARDS COMMITTEE P1788 FOR INTERVAL ARITHMETIC REQUIRES AN EXACT DOT PRODUCT
SN - 978-989-8425-06-5
AU - Kulisch U.
PY - 2010
SP - 475
EP - 478
DO - 10.5220/0002906204750478