Significance Arithmetic on the Ibm 7090 (Classic Reprint) - Softcover

Goldstein, Max

9781332093724: Significance Arithmetic on the Ibm 7090 (Classic Reprint)

Softcover

ISBN 10: 1332093728 ISBN 13: 9781332093724

Verlag: Forgotten Books, 2018

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Excerpt from Significance Arithmetic on the Ibm 7090

Section 1. Introduction. 2. Past Experience 3. Discussion of Rules 4. Computer Instructions 5. A Note on the Elementary Functions. 6. Use of the Significance Mode. 7. Numerical Experiments using Significance Mode 8. Conclusions Acknowledgements. References.

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Excerpt from Significance Arithmetic on the Ibm 7090

I. Introduction.

Scientific computations, except for problems in which no scaling is required or for certain specialized problems which deal with rational numbers only, are generally handled on machines in the floating point notation. This notation affords great range and simplicity of programming.

It would be difficult to deny the efficacy of automatic floating point operations as a means for eliminating the rescalling procedures of fixed point computing. But at what price has this convenience been bought? In the era of fixed point computing we knew that our results were more or less justifiable on the basis of all reasonable criteria for judging the number of significant places in a result. Now popular normalized floating point calculations simply avoid the embarrassment of improperly scaled fixed point operations and simultaneously obscure the possibility that the results may be nonsense, because non-significant digits have been introduced at some stages of the computation. It would seem that automatic procedures could be useful for determining whether cancellation has indeed destroyed the usefulness of a result.

Several methods have been suggested for possible incorporation into the hardware of computers to aid in the estimation of significance.

About the Publisher

Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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