Articles or book(s) about the functions behind a scientific calculator

10202017, 06:53 PM
(This post was last modified: 10202017 06:55 PM by pier4r.)
Post: #1




Articles or book(s) about the functions behind a scientific calculator
Since I am packing some information in the hp calc torrent I started to read more properly some of the contents (not only skimming them).
The article about the SOLVE function of the 34C is really neat ( hp journal 1980.08). From this article, aside from computing the following \( \int_{0}^{1} \frac{du}{1  u^{64}} \) ( that is taking ages on the sharp el506w, with n=10000 so a single step is [10]/10000 . I want to compare it with the 200 seconds mentioned for the 34C ); I was saying, aside from computing the formula above, a question popped in my head: whether do articles or books that explains the algorithms behind an entire scientific calculator exists. (a scientific calculator is enough, a graphing/programmable may be overkill) I know that one could connect the math theory of functions to those actually implemented in a scientific calculator, plus numerical algorithms are explained somewhere in some journals. Nevertheless the choices about the math functions to pack in a calculator, with limited resources, may contain subtle and neat observations that would be interesting to know. Exactly like the article in the mentioned hp journal. I am asking about a book because the source code of the algorithms may be not that readable, unless there are plenty of comments. Furthermore if the source coude would be enough, I am not sure about the code of Hp, casio, sharp, ti scientific calculators; but the wp31 or wp34 would help I guess, since their code is open as far as I know. Wikis are great, Contribute :) 

10212017, 07:35 AM
(This post was last modified: 10212017 07:37 AM by Dan.)
Post: #2




RE: Articles or book(s) about the functions behind a scientific calculator
I too was looking for such a book but could not find one. I referred to the attached articles to code in assembly CORDIC algorithms for the scientific functions on the AriCalculator. Overall they work quite well but there is room for improvement, particularly for the trig functions. See my post at the end of page 3 for some calculation results:
http://www.hpmuseum.org/forum/thread7773page3.html 

10212017, 08:21 AM
Post: #3




RE: Articles or book(s) about the functions behind a scientific calculator
Thanks for sharing and thanks for linking the thread. It is exactly on the point.
Impressive how a slight change in interest changes the value of what we perceive. Some days ago I would have valued the linked thread interesting, but not in the direction that I wanted to follow, and now instead I find it mentioning a lot of things I would like to read/check. Wikis are great, Contribute :) 

10212017, 12:22 PM
Post: #4




RE: Articles or book(s) about the functions behind a scientific calculator
I found this book last year, the examples given run on a TI calculator but that is not necessary to understand the algorithms. "Inside Your Calculator, From Simple Programs to Significant Insights" by Gerald R. Rising, published by WILEY, ISBN 9780470114018. It covers many algorithms, including CORDIC.
Check out NQ41! 

10212017, 01:00 PM
(This post was last modified: 10232017 10:50 AM by pier4r.)
Post: #5




RE: Articles or book(s) about the functions behind a scientific calculator
(10212017 07:35 AM)Dan Wrote: cut checked the HP.pdf you find also the articles of william kahan quite informative. See: hp journal December 1979 and Hp journal August 1980 Craig, thanks for your input. I check! Wikis are great, Contribute :) 

10232017, 09:38 AM
Post: #6




RE: Articles or book(s) about the functions behind a scientific calculator
Hello,
I guess that the great "Mathematics written in sand" from W. kahan should also be checked. https://people.eecs.berkeley.edu/~wkahan/MathSand.pdf Regards Vincent 

10232017, 10:51 AM
(This post was last modified: 10252017 06:56 PM by pier4r.)
Post: #7




RE: Articles or book(s) about the functions behind a scientific calculator
Yup, integrated already in the hp calc collection . Thanks for the input!
Wikis are great, Contribute :) 

10232017, 01:04 PM
Post: #8




RE: Articles or book(s) about the functions behind a scientific calculator
At the risk of starting another minor flame war might I point out that Gerald Rising's book, mentioned above, is available on Libgen.


10232017, 04:38 PM
Post: #9




RE: Articles or book(s) about the functions behind a scientific calculator
(10232017 01:04 PM)rncgray Wrote: At the risk of starting another minor flame war might I point out that Gerald Rising's book, mentioned above, is available on Libgen. On Rising's own web page, I see no indication that his book is in the public domain, which would suggest any copy in Libgen is illegal. 

10242017, 09:24 AM
(This post was last modified: 10242017 09:24 AM by Dan.)
Post: #10




RE: Articles or book(s) about the functions behind a scientific calculator  
10252017, 06:55 PM
Post: #11




RE: Articles or book(s) about the functions behind a scientific calculator
HP Journal May 1983, when talking about the 15C, gives quite some inputs too.
Wikis are great, Contribute :) 

07282018, 07:45 AM
Post: #12




RE: Articles or book(s) about the functions behind a scientific calculator
I recommend Scientific Analysis on the Pocket Calculator, by Jon Smith


07282018, 04:25 PM
(This post was last modified: 07282018 04:25 PM by SlideRule.)
Post: #13




RE: Articles or book(s) about the functions behind a scientific calculator
for CORDIC:
a: High Precision and High Speed handheld Scientific Calculator Design using hardware based CORDIC Algorithm [Science Direct] b: Assembly Code to Compute Sine and Cosine using the CORDIC Algorithm [NISTR 4480] c: Implementing CORDIC Algorithms [Dr Dobbs Journal v15] Lottsa articles, etc. using SE with CORDIC + calculator as search term. BEST! SlideRule 

07292018, 03:38 PM
Post: #14




RE: Articles or book(s) about the functions behind a scientific calculator
Thank you for the CORDIC article references, SlideRule.


07292018, 07:41 PM
Post: #15




RE: Articles or book(s) about the functions behind a scientific calculator
(07282018 07:45 AM)Albert Chan Wrote: I recommend Scientific Analysis on the Pocket Calculator, by Jon Smith This BOOK is excelent, thanks for the free link to download the complete book. I have boght it around 1980, the number of pages is next to 400. Pedro 

08012018, 02:39 AM
Post: #16




RE: Articles or book(s) about the functions behind a scientific calculator
I would suggest The Art of Computer Programming, by Donald Knuth, especially Volume 1 Chapter 1 and Volume 2 Chapter 2.


08012018, 11:41 AM
Post: #17




RE: Articles or book(s) about the functions behind a scientific calculator
Knuth is  comprehensive. But not always easy to follow.
There's a section in Volume 2, on factoring prime numbers [and Fermat, I think] that make my eyes glaze over every time i try to read it. A book on calculator algorithms is a fine idea, but what level of math prowess do you expect of the target audience? 

08052018, 11:22 AM
Post: #18




RE: Articles or book(s) about the functions behind a scientific calculator
Doesn't matter. The more sources (hard or easy, anyway always full of info) the better. The reader will decide which one are usable.
Wikis are great, Contribute :) 

08252018, 12:27 PM
(This post was last modified: 08262018 06:51 PM by pier4r.)
Post: #19




RE: Articles or book(s) about the functions behind a scientific calculator
This other thread is related: http://www.hpmuseum.org/forum/thread11212.html
Would be nice if we could edit, collaboratively, "suggested related threads" to some threads. On a side node, the MyBB search function worked better than google, and it is the second time! Of course one should have quite good keywords. Wikis are great, Contribute :) 

08262018, 10:05 AM
(This post was last modified: 08262018 11:15 AM by sasa.)
Post: #20




RE: Articles or book(s) about the functions behind a scientific calculator
(08252018 12:27 PM)pier4r Wrote: Would be nice if we could edit, collaborative, "suggested related threads" to some threads. Yes, it would be interesting. I have thought some time ago to make here a series of articles about formulas and algorithms I used in my math lib (after long process of research and testing from many sources). They are rather suitable for microcontrollers and IEEE754 floating point (both 32 and 64bit). However, for early BCD based chips used in calculators, suitable algorithms are a bit different and much slower due extremely limited resources, on the contrary very cheap nowadays MCUs have. Specialized books are still not cheap sources and often even Wikipedia (internet in general) have good enough sources for this purpose... Today, calculator manufacturers rather keep all used algorithms closed, under intellectual property rights, on the contrary as that was the case in pioneer days. Good resource for advanced research as well are open source CAS libraries. 

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