Skip to main content Accessibility help
×
Home
Hostname: page-component-768dbb666b-sz752 Total loading time: 1.782 Render date: 2023-02-04T20:04:34.143Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

2 - Computer Arithmetic

Published online by Cambridge University Press:  01 June 2011

John F. Monahan
Affiliation:
North Carolina State University
Get access

Summary

Introduction

Most of the time, we wish to be blissfully ignorant of the inner workings of any complicated machine. When we drive an automobile, traffic and road conditions demand our concentration, and we would prefer that our attention wander to a favorite song on the radio than to the oil pressure gauge. Only when trouble arises need we concern ourselves with the internal combustion engine, air pressure in the tires, the lever arms in the steering system, or a lug wrench. With as complicated a machine as a computer, most of the time we can likewise treat its inner workings as a collection of black boxes. However, researchers regularly operate a computer at its limits in the same way a race-car driver takes an automobile to the limits of its capabilities. In order to drive safely bumper-to-bumper at 200 mph, a race-car driver must understand the operation of every system of the machine. A researcher must understand the inner workings of the arithmetic of the computer; otherwise, Overflow and Underflow become mysterious demons. Knowledge will not only dispel the fears brought on by ignorance, it will also permit the researcher to control his or her computational destiny and not fall victim to “roundoff error” any more than to “racing luck.”

The first three sections of this chapter present a brief overview of the mechanics of computer arithmetic. Although necessary for ground-level knowledge, they should be skimmed at first reading because the interesting details of the problems can easily sidetrack the reader.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alefeld, Gotz and Herzberger, Jurgen (1983), Introduction to Interval Computations. New York: Academic Press.Google Scholar
Alfeld, Peter and Eyre, David J. (1991), “The Exact Analysis of Sparse Rectangular Systems,” ACM Transactions on Mathematical Software 17: 502–18.CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Computer Arithmetic
  • John F. Monahan, North Carolina State University
  • Book: Numerical Methods of Statistics
  • Online publication: 01 June 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511977176.004
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Computer Arithmetic
  • John F. Monahan, North Carolina State University
  • Book: Numerical Methods of Statistics
  • Online publication: 01 June 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511977176.004
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Computer Arithmetic
  • John F. Monahan, North Carolina State University
  • Book: Numerical Methods of Statistics
  • Online publication: 01 June 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511977176.004
Available formats
×