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Literature suggestions about numerical errors on calculators
03-18-2020, 01:41 PM
Post: #1
Literature suggestions about numerical errors on calculators
Hello,
the book "Rounding errors in algebraic processes" by Wilkinson is a good read but it's way out of date.
IEEE-754 is now the thing for both radix 2 and 10. Also there certainly are proceedings on this topic in 50 years.
Can anyone suggest up-to-date/more modern books which are easy to read?
"Accuracy and Stability of Numerical Algorithms" by Higham seems to go this way but might be too in-depth.
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03-18-2020, 02:52 PM (This post was last modified: 03-18-2020 02:55 PM by BobVA.)
Post: #2
RE: Literature suggestions about numerical errors on calculators
The HP-15C Advanced Functions Handbook has a good, easy-to-read discussion of this topic (Appendix: Accuracy of Numerical Calculations). It doesn't specifically discuss IEEE 754 though.
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03-18-2020, 04:04 PM
Post: #3
RE: Literature suggestions about numerical errors on calculators
(03-18-2020 01:41 PM)erazor Wrote:  Hello,
the book "Rounding errors in algebraic processes" by Wilkinson is a good read but it's way out of date.
IEEE-754 is now the thing for both radix 2 and 10. Also there certainly are proceedings on this topic in 50 years.
Can anyone suggest up-to-date/more modern books which are easy to read?
"Accuracy and Stability of Numerical Algorithms" by Higham seems to go this way but might be too in-depth.

Have you seen the Wikipedia entry? If not, go here:

https://en.wikipedia.org/wiki/Floating-p..._rationale

Tom L
...other than that, Mrs. Lincoln, what did you think of the play?
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03-18-2020, 04:26 PM
Post: #4
RE: Literature suggestions about numerical errors on calculators
Goldberg: "What every computer scientist should know about floating point"
https://dl.acm.org/doi/10.1145/103162.103163

I think it is all summed up by Kernigham and Plauger in "Elements of Programming Style": "Working with floating point is like moving sand piles. Every time you move one you lose a little sand and pick up a little dirt".
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03-18-2020, 09:42 PM (This post was last modified: 03-18-2020 09:45 PM by SlideRule.)
Post: #5
RE: Literature suggestions about numerical errors on calculators
An excerpt from Computer Arithmetic and Validity Theory, Implementation, and Applications 2e, De Gruyter, © 2013, e-ISBN 978-3-11-030179-3

Introduction (pg. 3)
  "The task of numerical analysis is to develop and design algorithms which use floating-point numbers to deliver a reasonably good approximation to the exact result. An essential part of this task is to quantify the error of the computed answer. Managing this quite natural error is the crucial challenge of numerical or scientific computing. In this respect, numerical analysis is completely irrelevant to everyday applications of computers like those mentioned in the opening paragraph of the Preface. For solving problems of this kind, integer arithmetic, which is exact, is used, or should be, whenever arithmetic is needed."

Emphasis mine.

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SlideRule

/əˈriTHməˌtik/
the branch of mathematics dealing with the properties and manipulation of numbers.
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03-19-2020, 05:45 AM
Post: #6
RE: Literature suggestions about numerical errors on calculators
Thanks for the suggestions.
Posting the link to the HP-15c advanced functions manual.
The Goldberg article is available to the public in an edited version from Oracle.
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03-19-2020, 09:49 AM
Post: #7
RE: Literature suggestions about numerical errors on calculators
(03-18-2020 04:04 PM)toml_12953 Wrote:  
(03-18-2020 01:41 PM)erazor Wrote:  Hello,
the book "Rounding errors in algebraic processes" by Wilkinson is a good read but it's way out of date.
IEEE-754 is now the thing for both radix 2 and 10. Also there certainly are proceedings on this topic in 50 years.
Can anyone suggest up-to-date/more modern books which are easy to read?
"Accuracy and Stability of Numerical Algorithms" by Higham seems to go this way but might be too in-depth.

Have you seen the Wikipedia entry? If not, go here:

https://en.wikipedia.org/wiki/Floating-p..._rationale

There are some great writings by Kahan, and some of them are linked as footnotes from that Wikipedia article section.
How Java's floating-point hurts everyone everywhere (PDF)
Why do we need a floating-point arithmetic standard? (PDF)
The Baleful Effect of Computer Benchmarks upon Applied Mathematics, Physics and Chemistry (PDF)
Marketing versus Mathematics (PDF)

Also, from his own web site:
Mathematics Written in Sand (PDF)

Also of interest:
Severance, Charles (1998-02-20). "An Interview with the Old Man of Floating-Point".
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