Literature suggestions about numerical errors on calculators

03182020, 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the book "Rounding errors in algebraic processes" by Wilkinson is a good read but it's way out of date. IEEE754 is now the thing for both radix 2 and 10. Also there certainly are proceedings on this topic in 50 years. Can anyone suggest uptodate/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 indepth. 

03182020, 02:52 PM
(This post was last modified: 03182020 02:55 PM by BobVA.)
Post: #2




RE: Literature suggestions about numerical errors on calculators
The HP15C Advanced Functions Handbook has a good, easytoread discussion of this topic (Appendix: Accuracy of Numerical Calculations). It doesn't specifically discuss IEEE 754 though.


03182020, 04:04 PM
Post: #3




RE: Literature suggestions about numerical errors on calculators
(03182020 01:41 PM)erazor Wrote: Hello, Have you seen the Wikipedia entry? If not, go here: https://en.wikipedia.org/wiki/Floatingp..._rationale Tom L Cui bono? 

03182020, 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". 

03182020, 09:42 PM
(This post was last modified: 03182020 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, eISBN 9783110301793
Introduction (pg. 3) "The task of numerical analysis is to develop and design algorithms which use floatingpoint 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. BEST! SlideRule /əˈriTHməˌtik/ the branch of mathematics dealing with the properties and manipulation of numbers. 

03192020, 05:45 AM
Post: #6




RE: Literature suggestions about numerical errors on calculators
Thanks for the suggestions.
Posting the link to the HP15c advanced functions manual. The Goldberg article is available to the public in an edited version from Oracle. 

03192020, 09:49 AM
Post: #7




RE: Literature suggestions about numerical errors on calculators
(03182020 04:04 PM)toml_12953 Wrote:(03182020 01:41 PM)erazor Wrote: Hello, There are some great writings by Kahan, and some of them are linked as footnotes from that Wikipedia article section. How Java's floatingpoint hurts everyone everywhere (PDF) Why do we need a floatingpoint 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 (19980220). "An Interview with the Old Man of FloatingPoint". 

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