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

[pier4r]

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 [1-0]/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.

[Dan]

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/thread-7773-page-3.html

[pier4r]

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.

[Craig Bladow]

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 978-0-470-11401-8. It covers many algorithms, including CORDIC.

[pier4r]

(10-21-2017 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!

[Vincent]

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

[pier4r]

Yup, integrated already in the hp calc collection . Thanks for the input!

[rncgray]

At the risk of starting another minor flame war might I point out that Gerald Rising's book, mentioned above, is available on Libgen.

[Thomas Okken]

(10-23-2017 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.

[Dan]

(10-23-2017 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.

Wow. The Encyclopedia Galactica is finally here.

[pier4r]

HP Journal May 1983, when talking about the 15C, gives quite some inputs too.

[Albert Chan]

I recommend Scientific Analysis on the Pocket Calculator, by Jon Smith

[SlideRule]

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

[rncgray]

Thank you for the CORDIC article references, SlideRule.

[PedroLeiva]

(07-28-2018 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

[NetMage]

I would suggest The Art of Computer Programming, by Donald Knuth, especially Volume 1 Chapter 1 and Volume 2 Chapter 2.

[sa-penguin]

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?

[pier4r]

Doesn't matter. The more sources (hard or easy, anyway always full of info) the better. The reader will decide which one are usable.

[pier4r]

This other thread is related: http://www.hpmuseum.org/forum/thread-11212.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.

[sasa]

(08-25-2018 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 IEEE-754 floating point (both 32 and 64-bit). 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.