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

08272018, 08:29 AM
Post: #21




RE: Articles or book(s) about the functions behind a scientific calculator
(08262018 10:05 AM)sasa Wrote: 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. I used BCD and CORDIC algorithms in the firmware I recently completed for the AriCalculator. I will rewrite the algorithms for multiplication and division using the multiplication and division assembly instructions (I used shift and add algorithms in the original firmware), but I think CORDIC algorithms are the best option for the transcendental functions for microcontrollers without a floatingpoint coprocessor. 

11232018, 03:03 PM
(This post was last modified: 11232018 03:04 PM by SlideRule.)
Post: #22




RE: Articles or book(s) about the functions behind a scientific calculator
An eclectic, pedagogical tome (perhaps) & apropos …
An Analysis of Algorithms for Hardware Evaluation of Elementary Functions Richard Franke NAVAL POSTGRADUATE SCHOOL Monterey, CA "Abstract: Algorithms for the automatic evaluation of elementary functions were studied. Available algorithms obtained from current literature were analyzed to determine their suitability for hardware implementation, in terms of their accuracy, convergence rate, and hardware requirements. The functions considered were quotient, arctangent, cosine/sine, exponential, power function, logarithm, tangent, square root, and product". A decent SE should locate the web repository. BEST! SlideRule 

11232018, 04:54 PM
Post: #23




RE: Articles or book(s) about the functions behind a scientific calculator
First hit here looks right. Thanks!
(11232018 03:03 PM)SlideRule Wrote: An eclectic, pedagogical tome (perhaps) & apropos … 

11232018, 05:04 PM
Post: #24




RE: Articles or book(s) about the functions behind a scientific calculator  
11232018, 06:00 PM
(This post was last modified: 11232018 09:11 PM by SlideRule.)
Post: #25




RE: Articles or book(s) about the functions behind a scientific calculator
Chapter 7 The CORDIC Algorithm (pgs 133156) of Elementary Functions algorithms & implementation 2e by JeanMichel Muller {© 2006 Birkhäuser} may also be of interest.
excerpt from Chapter 1 This book is devoted to the computation of the elementary functions. Here, we call elementary functions the most commonly used mathematical functions: sin, cos, tan, sin⁻¹, cos⁻¹, tan⁻¹, sinh, cosh, tanh, sinh⁻¹, cosh⁻¹, tanh⁻¹, exponentials, and logarithms (we should merely say “elementary transcendental functions”: from a mathematical point of view, ¹/x is an elementary function as well as e^x. We do not deal with the basic arithmetic functions in this book). Theoretically, the elementary functions are not much harder to compute than quotients: it was shown by Alt [4] that these functions are equivalent to division with respect to Boolean circuit depth. This means that, roughly speaking, a circuit can output n digits of a sine, cosine, or logarithm in a time proportional to log n (see also Okabe et al. [249], and Beame et al. [25]). For practical implementations, however, it is quite different, and much care is necessary if we want fast and accurate elementary functions. BEST! SlideRule 

11252018, 06:11 AM
Post: #26




RE: Articles or book(s) about the functions behind a scientific calculator
Nice. I'm also looking for info on algorithms for solving equations. I think HP journal from late 70's, early 80's had some articles about that. Also looking to write an editor for entering equations for the solver and for graph sketching, e.g. typing x^2 + 1 results in ENTER 2 ^ 1 + . I recall seeing flowcharts from expired HP patents, but not sure if it was for an editor or something else.


11252018, 11:21 AM
Post: #27




RE: Articles or book(s) about the functions behind a scientific calculator
(11252018 06:11 AM)Dan Wrote: .... Also looking to write an editor for entering equations for the solver and for graph sketching, e.g. typing x^2 + 1 results in ENTER 2 ^ 1 + . I recall seeing flowcharts from expired HP patents, but not sure if it was for an editor or something else. https://en.m.wikipedia.org/wiki/Shuntingyard_algorithm 

11252018, 02:52 PM
Post: #28




RE: Articles or book(s) about the functions behind a scientific calculator
Is this project language dependent, ie JAVA, C++, etc? If not, I suggest FORTH as a basis … FORTH Dimension … magazine …
[attachment=6626] vol3_no6_pgs11 … cont.12 … [attachment=6625] vol4_no6_pg14 … etc. A decent SE should locate the webarchives of the entire series. BEST! SlideRule 

11252018, 06:57 PM
Post: #29




RE: Articles or book(s) about the functions behind a scientific calculator
(11252018 06:11 AM)Dan Wrote: Also looking to write an editor for entering equations for the solver and for graph sketching, e.g. typing x^2 + 1 results in ENTER 2 ^ 1 + . On the HP48 you can install examples by executing the TEACH command. They are installed in a new directory EXAMPLES. Further down in PRGS is a program →RPN that allows to translate algebraic expressions to RPN. Example: 'X^2+1' →RPN { X 2 ^ 1 + } And then there's the AECROM module for the HP41 that allows to generate program code based on an equation: Example: PROG EXAMPLE ENTER:FORMULA X↑2+1 R/S ENTER:LBL,CONS X . .= R/S ANS= R/S PROGRAMMING. . PACKING RUN SIZE>=01 This results in the following program: Code: LBL "EXAMPLE" How cool is that? Cheers Thomas 

11252018, 07:45 PM
Post: #30




RE: Articles or book(s) about the functions behind a scientific calculator
Addendum:
A while ago I've written a Python to FOCAL Compiler. The program is still online: just click run ▸ and define your function. Code: def example(x): And then run: Code: translate(example.__code__) This will produce the following HP41 program: Code: LBL "EXAMPLE" And then there's tcab's fancy Python to RPN  source code converter. It will translate: Code: LBL("EXAMPLE") Code: LBL "EXAMPLE" HTH Thomas 

11272018, 12:02 AM
Post: #31




RE: Articles or book(s) about the functions behind a scientific calculator
Thanks Will, SlideRule and Thomas. The "shuntingyard" algorithm by Dijkstra for converting infix to postfix is exactly what I am looking for. It's for the AriCalculator, which I am writing in assembly.


11282018, 11:05 AM
Post: #32




RE: Articles or book(s) about the functions behind a scientific calculator
Dear All,
thanks for sharing the link to the "shuntingyard" algorithm. After reading the article I searched for further sources about the the topic and found this article which sheds some light upon the time and process when the stack machine and the reverse polish notation was developed. Enjoy. Best regards Karl 

11282018, 04:37 PM
Post: #33




RE: Articles or book(s) about the functions behind a scientific calculator
(11282018 11:05 AM)KarlLudwig Butte Wrote: …thanks for sharing the link to the "shuntingyard" algorithm …. I searched for further sources … found … this article … when the stack machine and the reverse polish notation was developed … Karl A modest SE query should locate this manual for the KDF9 [attachment=6642] for further edification. BEST! SlideRule 

11292018, 03:40 AM
Post: #34




RE: Articles or book(s) about the functions behind a scientific calculator
(11282018 04:37 PM)SlideRule Wrote: A modest SE query should locate this manual for the KDF9 According to Wikipedia, the KDF9 "weighed more than 10,300 pounds (5.2 short tons; 4.7 t). Control desk with interruption typewriter 300 lb (136 kg), main store and input/output control unit 3,500 (1,587 kg), arithmetic and main control unit 3,500 (1,587 kg), power supply unit 3,000 (1,360 kg)." 

11292018, 08:16 AM
Post: #35




RE: Articles or book(s) about the functions behind a scientific calculator
Quote:A modest SE query should locate this manual for the KDF9Hi SlideRule, I have found the KDF9 Programming Manual at the WaybackMachine (aka archive.org). Unfortunately the file format is djvu but this can be converted online with an online converter especially for this case. By the way, what do you mean by "A modest SE query..."? Best regrds Karl 

11292018, 09:08 AM
Post: #36




RE: Articles or book(s) about the functions behind a scientific calculator
(11292018 08:16 AM)KarlLudwig Butte Wrote:Quote:A modest SE query should locate this manual for the KDF9By the way, what do you mean by "A modest SE query..."? SE query... Search Engine query. I wouldn't exactly have called it modest though. I'd never heard of either ICL or the KDF9. (Post 320) Regards, BrickViking HP50g Casio fx9750G+ Casio fx9750GII (SH4a) 

11292018, 12:30 PM
Post: #37




RE: Articles or book(s) about the functions behind a scientific calculator
(11292018 09:08 AM)brickviking Wrote:(11292018 08:16 AM)KarlLudwig Butte Wrote: By the way, what do you mean by "A modest SE query..."? Hi Brickviking, if you are generally interested in computer history, you can use this as a pretext to dive into British computer history. Along the way you'll meet the Cambridge Computer Lab's EDSAC computer and its builder Maurice Wilkes, meet the first Office Computer LEO built by Oliver Standingford, Raymond Thompson and David Caminer at J. Lyons and Co. (and perhaps read the highly recommended book "A Computer named Leo" by Georgina Ferry), and finally arrive at ICL and KDF9, descendants of LEO and Leo Computers Ltd. Best regards Karl P.S. Use the underlined words as search words and you'll find plenty of information. 

11292018, 01:12 PM
Post: #38




RE: Articles or book(s) about the functions behind a scientific calculator
(11292018 12:30 PM)KarlLudwig Butte Wrote: … interested in computer history … British computer history … (and perhaps read the highly recommended book "A Computer named Leo" by Georgina Ferry), … I queried for A Computer named Leo and was presented with A Computer Called Leo in reply. BEST! SlideRule 

11292018, 01:42 PM
Post: #39




RE: Articles or book(s) about the functions behind a scientific calculator  
11292018, 02:11 PM
Post: #40




RE: Articles or book(s) about the functions behind a scientific calculator
(11292018 01:42 PM)SlideRule Wrote: The reference archive generally offers multiformat retrieval, I recommend the Torrent option for a PDF. Even simpler: Shorten the url to: https://web.archive.org/web/201707010706.../Documents which presents an unformatted page with a list of documents, including the desired document in PDF format for direct download. A nice (intended?) sideeffect of how archive.org renders content; works for many, but not all, pages in the archive. Bob Prosperi 

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