The Museum of HP Calculators

HP Forum Archive 13

[ Return to Index | Top of Index ]

what is your favorite (YOUR OWN) RPN program?
Message #1 Posted by bill platt on 15 Nov 2003, 3:50 p.m.

I post this question because it will hopefully help to give us all a better idea of:

a: what sorts of things we use our calculators for,

b: why RPN is good (or why keystoke programming in general)

c: why BASIC and other methods are good (Valentin, please feel free to post your favorite non RPN, too!:-))

Be sure that you describe a program that *you yourself* wrote--not something you got out of a book, or modified from someone else. It *has* to be your very own thing.

And it does not have to be big. It does not have to be complex. It it doesn't have to be THE one (we change our minds and perceptions with time, right!). And it does not have to be your latest (mine isn't). But it has to be satisfying--or really effective in your mind (tell us why).

So here goes: my favorite (for the time being) is one that I wrote to compute the 2nd moment of areas of arbitrary rectangular sections, along with adding known arbitrary shapes with known area, centroid, and fundamental 2nd moment about centroid, t oa set of other known shapes or rectangles. In this case, I discovered later that there was some sort of program in the calculator manual that did this--but I didn't bother to look, and I knew what I wanted! and besides, it is *sooooo* much more satisfying to give it a try all on ones own occasionally....

The reason this is such a satisfying program is that if you do mechanical design, and you need to know what the bending stress will be of some arbitrary set of parts, you need to know the "inertia" or "second moment of area" and the "Section modulus" of that section. While yes, I also wrote a spreadsheet program that does this task, the calculator is both "safer" in a way (no cells to mangle etc), but also portable, fast, there with pencil and paper as you are sketching and playing with ideas....And to have it programmed in, rather than doing it by hand, save lots of time! If yo uhave never done this computation, it goes like this:

Area y A*y A*y^2 I

Area2 y2 A2*y2 A2*y2^2 I2

Sum A Sum Ay (SumAy^2)+(Sum I)= Ib

SumAy / sUMA = Y'

Ib - (A*Y'^2) = I about centroid.

Z = section modulus = I / (max fiber - centroid position).

So, you can see that there is a lot of button pressing!

Further, in RPN, it programmed very smoothly--not very different from doing the problem by hand (except all the registers). So, that was satisfying.

Maybe I'll post the code later---but you don't have to post your code---better to get us talking about what we are doing first, not yet how we do it.

Basically, I have a "clear" routine (which is handy for preserving the contents of registers that are in use in other programs--rather than clearing the whole machine's registers), a "rectangles" entry routine, a "summing for I and Z" routine, and a routine for input of known sections (which always must be followed with the "summing" routine).

Best regards, and looking forward to hearing some fun stories!

-Bill Platt

Edited: 15 Nov 2003, 4:58 p.m.

Re: what is your favorite (YOUR OWN) RPN program?
Message #2 Posted by Andrés C. Rodríguez (Argentina) on 15 Nov 2003, 7:24 p.m.,
in response to message #1 by bill platt

For HP 25, prime number tester or factor finder; and battleship game.

For HP 41: Space Shuttle Landing Simulator (sort of game) and RCA 1802 microprocessor cross assembler (very crude, I admit)

I have some partial listings of the above, and have planned for months a detailed article on the last two, but I have not found the time to advance with such project...

Re: what is your favorite (YOUR OWN) RPN program?
Message #3 Posted by jimc (can.) on 15 Nov 2003, 11:11 p.m.,
in response to message #1 by bill platt

My favourite is my drilling fluids rheology program. When I was an engineer on the drilling rigs in the 80's, we had slide rules to calculate pressure drops, viscosities, and flow regimes. Using my trusty HP, I wrote a program using a procedure that I continue to use today - that is, define the parameters the user may wish to change, and attach them to a a Lbl instruction. In this way the user could examine several what if scenarios. It forced me to examine a structured programming sequence. To do it though, required over 600 steps. I was grateful for the continuous memory!

While I was using this program (in about 1/5 the time my fellow engineers were doing it using the company supplied slide rules) I was able to finish my am reports, complete with calculations for solids, weight up requirements, and relevant costs. At the time, it was a marvelous time saver.

Sure, its old tech. But then, so are Louis Armstrong's recordings....That doesn't mean it is any less relevant today. Any open minded person can enjoy it!


Re: what is your favorite (YOUR OWN) RPN program?
Message #4 Posted by Jim Chumbley on 17 Nov 2003, 9:08 a.m.,
in response to message #3 by jimc (can.)


Would you please state the machine you ran this program on? I presume it was the HP-41C/CV. And would you explain how you managed the 600 program steps? I am imagining that it was designed as subroutines swapped in and out of working memory.

Edited: 17 Nov 2003, 9:09 a.m.

Re: what is your favorite (YOUR OWN) RPN program?
Message #5 Posted by jimc on 17 Nov 2003, 2:33 p.m.,
in response to message #4 by Jim Chumbley

Hi Jim. Thanks for your post.

I used a 41 CX, and I reduced the size of the memory registers to less than 50 at start up so I had extra room for all of it. (its kind of fuzzy now, but I believe that this was one of my first errors) - anyway, I did this in about the first ten steps. Since some of the calculations were to be used separately, I wrote some external programs that were called into the main program. As the program grew, I tried to pare it down to where I could manage it.

Therefore, the large number of steps were about 1 program that used around 300 steps, and the other 10 or so programs using the remainder. Not technically one program, however, the external programs (or subroutines) were fairly useless without the main program, as the main program had the constants (prices, etc) that were "seeded" into the memory. This was one of those decisions that at first blush seemed sound, but upon reflection was fraught with difficulty.

Like I said in the original post, I learned a lot writing the program, however the fundamentals were sound enough that I continue to use them today. I am no longer a drilling guy - so I have had no use for the program. I planned on posting it to the 'net, but over the years it has gotten buried.....However, this thread has re-awakened my interest in digging through my old textbooks.

12345 deletes

Favorite RPN (and BASIC) programs [LONG]
Message #6 Posted by Valentin Albillo on 15 Nov 2003, 11:25 p.m.,
in response to message #1 by bill platt

Hi, Bill:

These are a few of my choicest ones for assorted HP handhelds (no SHARPs on sight):


WHAT: Numerical solution of 1st-order Differential Equations using a 3rd-order Runge-Kutta method

WHY: Because at the time, it seemed next to impossible to fit such a program on the meager HP-25's 49 steps, having to call your f(x) three times with different arguments and returning to different locations in a machine without GOSUB capability, while still leaving enough free steps to define your f(x).

My approach was clever enough that it inspired my close friend Fernando del Rey to try and improve it to a 4th-order RK method, which succeeded in calling f(x) *four* times, and still left 10 steps or so for your f(x). To this day I still consider it the most amazing program I've ever seen.


WHAT: Elliptical Filter Design

WHY: Elliptical Filters were superior to any other standard filters in that they can be of lower degree for a given specs, as they do have true minimax properties. Designing them requires elliptic trigonometric functions (instead of the usual circular ones) and computing them with the required accuracy and fast enough was a real challenge in the slow HP-67's 224 steps. I had to design quite clever algorithms to accomplish it all, but in the end my program would compute high-pass, low-pass, band-pass and band-stop elliptic filters, would compute the zeros and poles and would plot the graphics and all other data relevant to the design.


WHAT: 8x8 Othello (aka Reversi) game, the user playing against the HP-41C, which played a reasonably challenging game at a reasonably fast speed, while graphically printing the board, checking your moves for legality, being able to play against itself, and finally announcing the winner.

WHY: Because at the time noone had attempted to program such a complicated board game on a 41C. It required several Memory Modules (no Quad Module or 41CV then) and extremely impressed everyone who saw it, so much so that local HP used it to increase sales at local trade shows, as a demo, and it finally got to the hands of HP Corvallis, who where equally impressed. They wrote me a letter telling me so, and asking for my written permission to use and publish it as they saw fit, which I obligued. They then wrote a second 'thankyou' letter including a printed 'Outstanding Achievement' Diploma, redeemable for some expensive 41C peripherals. I still keep it. 'Othello' was also a sensation when I submitted it for publication in the legendary Australian PPC Technical Notes, where it appeared. Oddly, it had been previously submitted to PPC proper, but Richard Nelson gave it a miss.


WHAT: Trigonometric functions package

WHY: Because noone else had written an acceptable package which implemented all six trigonometric functions for the HP-12C under serious, strict requirements of accuracy and speed. Some people had tried before and after, but hastily and carelessly implementing a bunch of run-of-the-mill Taylor Series expansions doesn't quite cut it and is bound to offer poor accuracy and unacceptable running times or even outright errors for large arguments or arguments near extremes, i.e.: it's not the same computing arc tan(100000000) than arc tan(1), and it's not the same computing arc sin(0.99999) than arc sin(0.1). My program succeeds in delivering accurate results for extended ranges at the fastest speeds and it does so for all six functions in a single 99-step program.

WHAT: Polynomial root finder and evaluator

WHY: Because this very small, 37 step program, succeded in using the financial functions available in the HP-12C well above and beyond their intended uses to provide the best and fastest polynomial root finder and evaluator among all Voyager series models (HP-15C included) and even faster than any pure RPN programs for the HP-41C. It could find any and all real roots of an Nth-degree polynomial, without any iterations in user code, and it could directly evaluate the polynomial for some given arguments, also without using any user code loops.


WHAT: Computing E up to 208 digits

WHY: I haven't written that many programs for the HP-15C but this I consider particularly worthy. While it is possible to compute E to more than 400 digits on the 15C, my program was intended to do it using matrix functions and matrix techniques, as a way of demonstrating what they could do. So, it made a good use of matrix addition to update the running total, and a novel use of the matrix Frobenius Norm operation to detect termination, as well as scalar matrix division to normalize the final result. You don't see matrix operations being used like this that often.


WHAT: Chess - Solving mate problems in N moves

WHY: Because it actually solved any chess problem of the 'White to play and mate in N moves' kind, in pure BASIC with no help from assembly language routines, using the powerful technique of *recursive* user defined functions that HP-71B's ultra-advanced BASIC language allows. There's also a neat trick on my part, defining and using variables *local* to the functions, which is something apparently not possible. The resulting program is quite complex, implements a full legal-move generator and recursive move-tree generator and evaluator and works for any number of moves N, subject only to time and memory constraints.

WHAT: Scramble

WHY: Because it implements a really challenging and enjoyable *video* game on the smallish HP-71B display. It uses a number of commands contained in my 4 Kb compilation of LEX words and succeeds in creating a very entertaining game in just a dozen lines of BASIC, with several levels of difficulty and an assortment of tunnels and obstacles that the user can add to easily, for extra-fun.

Best regards from V.

Re: Favorite RPN (and BASIC) programs [LONG]
Message #7 Posted by Angel Martin on 16 Nov 2003, 2:32 a.m.,
in response to message #6 by Valentin Albillo

Hola Valentin,

I remember fondly playing Othello on my 41 back then, it was (and still is) a truly amazing feat, one that best showcased the 41 system advantages so I wasn't surprised when HP acknowledged it as such. At least then they could recognize a masterpiece when they saw one.

Since you're an avid Chess aficionado (I'd dare to say you probably exceed such grading), I was wondering if you ever came across a full chess program written on the 41 by a Belgium gentleman by the name of Claude Roeltgen? He managed to create such an ingenious program that I'll always regard this as another incredible achievement. Mind you, it is painfully slow! but again, that's not the point at all.

I dissected the program to see how some things were done. It has synthetics galore, using precompiled GTOS to jump to non-existing labels (to save program lines), amazing manipulation of multi-byte instructions being used separately depending on the jump distance, etc.

Let me know by mail If you're curious, I'll be glad to send you a copy on mag cards.

Best wishes,, AM.

Link to Valentin's Othello program for the HP41
Message #8 Posted by Gene Wright on 16 Nov 2003, 7:47 a.m.,
in response to message #6 by Valentin Albillo

One of my favorite games. Changed to not require a card reader by inserting the storing of needed constants at the start of the program.


Actually, it's 'Othello 2'
Message #9 Posted by Valentin Albillo on 17 Nov 2003, 4:46 a.m.,
in response to message #8 by Gene Wright

Hi, Gene:

Thanks for your kind words and for featuring some of my game programs on your excellent site, but as you fully state in the heading, the program you feature there is not the original 'Othello' I was referring to, but a later version, 'Othello 2'. Matter of fact, 'Othello' was never published in PPC, because Richard Nelson did not deem it proper. He published instead 'Othello 2', at a much later date. The original Othello was published earlier in PPC Technical Notes, and eventually, at the request of HP Corvallis themselves, it was fully documented and submitted to the HP-41C's Users Library.

Anyway, what's the difference ? Isn't 'Othello 2 ' an improved version of original 'Othello', better in all respects ? Well, yes and no. On the one hand, it's a much more complex program, features two levels of play, and so can play better at times. On the other hand, the original Othello was much more elegant, did a lot in significantly fewer program steps, and didn't require a card reader at all, being capable of running in less RAM without external initialization. In other words, O1 was the real gem, IMHO, innovative, elegant and streamlined, a programmer's dream come true, while O2 was clumsier, less elegant, and didn't really make the point, as its only redeeming feature, a better level of play, required significant extra resources, didn't play that much better, and was slower by an order of magnitude or more, so it was pretty useless as a demo and you'd need a lot of patience to play against its 'improved' level, thus greatly diminishing the awe factor and the enjoyment.

Besides having a look at O2, available at your site, I'll heartily suggest anyone interested to try and get the original Othello as well. *That* is the program I consider one of my very best.

Best regards from V.

Message #10 Posted by Patrick on 16 Nov 2003, 5:35 p.m.,
in response to message #6 by Valentin Albillo

Are the HP-25 programs you've mentioned publicly accessible? I certainly would like to see the program you consider the most amazing you've ever seen!

Re: Favorite RPN (and BASIC) programs [LONG]
Message #11 Posted by Fernando del Rey on 16 Nov 2003, 6:32 p.m.,
in response to message #6 by Valentin Albillo

Valentín, thanks for your kind words in referring to my 4th order Runge-Kutta program for the HP-25. I certainly wouldn’t have done it, had I not been inspired by your 3rd degree program. It’s certainly one of the favourite programs I ever wrote, especially since I did now owe an HP-25 myself, and I wrote and ran the program “in my head”, but had to wait until we both tried it together in your machine and it ran perfectly on the first try! I don’t think I have achieved such a feat (first try perfect run) in my programming life ever again.

Funny thing is that there is an amazingly similar program in the software library here at the museum, and that one leaves 12 steps to code the function. But I think my program required less external initialization and no precautions to not alter the LAST X register between steps. I wish I had an HP-25 to try and compare both versions.

I also have very fond memories of a program I wrote on the HP-67 to solve systems of up to 7 linear equations in seven unknowns. This must have been 1977, and I was in engineering school (I was a classmate of Valentín). There was one particular day that I was not inspired solving a tough mechanics problem during a final exam. So I did it by brute force, which meant taking all the forces and momentum to set up a system of exactly seven linear equations which I solved with my handy HP-67. Of course, the teacher had no clue that such thing as a programmable calculator existed, so he thought my correct results had simply been copied from someone else. I had to show him that I had solved it with the calculator and he wasn’t too happy with my method, but he could do nothing but give me a minimal pass grade. Oh well, at least my trusty 67 saved me from a flunked final!

Re: Favorite RPN (and BASIC) programs [LONG]
Message #12 Posted by Fernando del Rey on 16 Nov 2003, 7:08 p.m.,
in response to message #11 by Fernando del Rey

Sorry, I meant to say that I did NOT owe an HP-25 myself.

Will you share it with us, Fernando?
Message #13 Posted by Patrick on 16 Nov 2003, 9:41 p.m.,
in response to message #12 by Fernando del Rey

I'd love to see your 4th order RK program on the HP-25!

Re: Will you share it with us, Fernando?
Message #14 Posted by Fernando del Rey on 17 Nov 2003, 2:22 a.m.,
in response to message #13 by Patrick

Sure, give me a couple of days and I'll post it.

...NOT OWN... dammit! (NT)
Message #15 Posted by FdR on 17 Nov 2003, 2:24 a.m.,
in response to message #12 by Fernando del Rey


Re: Favorite RPN (and BASIC) programs [LONG]
Message #16 Posted by Valentin Albillo on 17 Nov 2003, 4:59 a.m.,
in response to message #11 by Fernando del Rey

Fernando posted:

"Funny thing is that there is an amazingly similar program in the software library here at the museum, and that one leaves 12 steps to code the function. But I think my program required less external initialization and no precautions to not alter the LAST X register between steps. I wish I had an HP-25 to try and compare both versions."

I'm not sure if "funny" is the correct word here. When I first saw that program in the software library at the museum, it made me very suspicious. I remember submitting your original program to PPC, PPC TN, and many particular individuals at the time (25 years ago), but if I recall correctly, it never got published (RN strikes again ! :-)

However, facts are that it got somewhat disseminated, and I've always wondered if the person who 'wrote' and submitted the program actually in this forum's Library could perhaps get some 'inspiration' in a copy of your original. If that's not the case, my apologies, but both programs seem far too similar that a 'lucky coincidence' seems unlikely. Even if it were, yours would pre-date the other one by decades.

Best regards from V.

Re: Favorite RPN (and BASIC) programs [LONG]
Message #17 Posted by Fred Lusk (CS) on 19 Nov 2003, 10:21 p.m.,
in response to message #6 by Valentin Albillo


I can be just as long with my post, or even longer :-)

My favorite programs are ones I have written myself while I was in school or as part of my work as a civil engineer. This is not because I claim my programs are better than anyone else's--though I think my best programs are very good--it's because of the time I spent researching the subject of each program and the time I spent actually making the program work. There is great pleasure in both the learning and the accomplishment, and they're useful in my work. Of course, my wife doesn't understand the attraction one bit, but then I don't understand some of what she likes. Good thing we keep our mouths shut about these eccentricities!

In high school and college I wrote simple programs for my HP-55, the best one was probably an interpolation program for finding all of the contour lines between two spot elevations (think topographic maps). I wrote this for my Engineering Graphics course.

Later in college I bought an HP-34C and wrote several nice programs for different engineering subjects. I even wrote a 34C program on the fly during my Hydrology final to solve a complicated iteration…I listed the formulas, the program steps, my initial guesses, and the result, and I explained how the SOLVE feature worked (my professor used an HP-45 so I knew my approach would be OK)…I finished the test after only 45 minutes and ended up with the highest grade…the second person out took another hour. He was totally blown away when I told him what I had done. Of course, he used a TI!

However, my best programs are for the 41/42S series. I started with an HP-41CV and replaced it a couple of years later with an HP-41CX. I added an Advantage ROM the day they arrived at Lewis & Lewis in Ventura, CA (remember when local dealers actually knew something?). I have an HP-32SII and an HP-48G+, but my calculator of choice now - as it has been for 15 years - is my HP-42S.

I have written a number of interchangeable solution programs for hydraulics that are similar to the Time Value of Money program in the original HP-41C Solutions Book (I think that's the name), including: (1) HW (Hazen-Williams for pressure pipes) (2) MEQ (Mannings for pressure pipes) (3) SD/SWR (Mannings for open channel flow in pipes) (4) CANAL (Mannings for open channel flow in a rectangular, triangular, and trapezoidal channels) I also have several HP-42S solver routines that I use for simple interchangeable solutions where I don't need annotated results.

I use these four (and others) on both the 41 and 42S. Programs (1) and (2) also include an overlapping interchangeable solution for the continuity equation (Q=AV). I say "overlapping" because flow rate and pipe diameter are shared by both equations and I use a toggle to determine which equation to use to solve these variables. Program (1) is my most used program over the years. I wrote it about 20 years ago while my wife was having an ultra-sound before our first daughter was born. I actually "wrote" it in my head (I had no paper) and transcribed the 200+ steps when I got home. My memory was much better back then! Program (3) solves sewer flows in gpm and storm drain flows in cfs. Program (4) is interesting because I use the same iteration subroutine for two of the variables. A flag determines which one to iterate.

(5) My favorite program in terms of cleverness is probably FEET, the Feet-Inches-Fractions program I posted here a couple of years ago. For those of you who live metric (and I wish I was one), this may seem unimportant. But, to those of us who have to calculate this stuff, this program is a god-send. I wrote it nearly 20 years ago for a co-worker. The core of the program (the fraction reduction) was adapated from the PPC ROM. I later discovered a simpler way to handle other parts of the program, but I haven't gotten around to finishing the last 10% so I can post the improved version. In any event, y'all may find the original program interesting.

Other programs I wrote for the 41 and/or the 42S and that I use frequently include: (6) VINT (Vector Interpolation) - this is useful for interpolating between rows or columns in a table based on "index values." I wrote this to interpolate the tables in "Circular Concrete Tanks Without Prestressing" and "Rectangular Concrete Tanks" (both by the Portland Cement Association). (7) NGAS (Natural Gas Flow Calculations) - this program solves the isothermal-compressible flow equation for upstream or downstream pressures in one reach of a natural gas system. I have more general Excel and Mathcad versions that handle multiple pipes, but this is good for things like checking the service lateral to a natural gas engine. (8) HYDR (Rational Method Hydrology) - this program solves single basin hydrology using the Rational (Irrational???) Method using either the Kirpich or FAA equations for Time of Concentration.

My last HP-42S program I will describe is a program I wrote a couple of years ago for a basic Statistics class. I had never taken a stat course and was self taught for the things I needed and use (mainly linear regression). I signed up for a lower division, math-oriented stat class at the local junior college (believe it or not, there are non-math-oriented stat classes…my wife took one in college…it was very qualitative with only a little bit of math). Anyway, my class was taught by my old high school physics teacher, who was still sharp as a tack at age 77±. He was (I think) one semester away from his PhD in Psychology when WWII intervened, but was expert in many areas…except calculators (TI). He wanted to know why I was there, and I told him it was to pester him! Of course, I had an unfair advantage since I had more math behind me than any of the other students (he took me off the grading curve). Since it usually took me only 15-20 minutes to do each 90 minute mid-term, I had lots of time to kill. After a test on chi-squares and contingency tables, I wrote a nifty little 77-step program that makes great use of the HP-42S's matrix capabilities. The best part was it gave a great excuse to tease him about his affinity for TIs. As an aside, when I was a senior in high school, my American Government teacher asked me to determine the correlation between standardized reading scores and class scores for his group of students. My HP-55 was able to handle the regression for about 175 individual data points (student scores). I remember pointing out to my physics teacher that his SR-51 (I think) was internally crippled because TI limited n to 99 data points. He was not amused.

My favorite program by others is CAVES for the HP-41, though I haven't played it in quite a while. It's the ONLY program that got my wife to actually want to use my calculator. She was a child development major in college and never had a need for a real calculator.

I have also played OTHELLO, and remember it as a very good program.

Now you know the rest of the story.


Re: Favorite RPN (and BASIC) programs [LONG]
Message #18 Posted by Chris(FLA) on 20 Nov 2003, 2:03 p.m.,
in response to message #17 by Fred Lusk (CS)

My favorite program by others is CAVES for the HP-41, though I haven't played it in quite a while. It's the ONLY program that got my wife to actually want to use my calculator.

Same here with my wife. She really enjoyed that game and played it for many hours. She also used the 11C I got her that she mainly used for work to figure out sales tax % on orders she would take. Still have the 11C and it is in mint condition. Running on the same batteries for 18+ years. I asked her recently if I could have the 11C and I received a direct and stern NO!

I taught her RPN in about an hour one day and she was hooked. I had to get her the 11C, my 41 kept growing legs and moving. She is an HP'er. She says the same thing I do when I have to use an AOS calculator. "How do you use this thing", "This is too hard to use", "Where is an RPN HP when I need it", and I wrote many a program on a TI-59 before I found the HP world and the simplistic beauty of RPN.



Re: what is your favorite (YOUR OWN) RPN program?
Message #19 Posted by Trent Moseley on 15 Nov 2003, 11:38 p.m.,
in response to message #1 by bill platt


It's a long, long, story, back to slide rule days. It is mainly about astronomy (my avocation). When I got my mail order HP-25C I thought I died and went to heaven. But in my profession at that time it was all about TVM. It also became cruch time: I had to learn RPN. I wrote programs to suit my personal needs (regarding TVM this was before the 12C). All the info I took was from old textbooks. I then blew my wad on the 67. Wow! The upshot is I like to take ideas or formuals and put them down in RPN. Footnote: I bought a 48GX, could not figure out RPL and gave it to my wife's nephew. I now have tons of stuff in the 15C and 42S. Another PS: I bought a 16C from Educalc. I still dont't know what its all about (I even have Grapevine's "Easy Course") so I do my checkbook on it.


Re: what is your favorite (YOUR OWN) RPN program?
Message #20 Posted by Jim Chumbley on 16 Nov 2003, 5:03 a.m.,
in response to message #1 by bill platt

My favorite RPN program is the one I wrote in 1976 for the (stillborn) National Semiconductor NS-7100, which was not an RPN machine, because HP still held active patents then, but rather it was an algebraic machine.

My favorite RPN program is the Hewlett-Packard RPN-mode emulator I wrote using the NS-7100's own keyboard language. It had a stack that was nine registers high!

Nat'l Semi & HP patents on RPN
Message #21 Posted by Karl Schneider on 16 Nov 2003, 2:05 p.m.,
in response to message #20 by Jim Chumbley

Jim --

Was National Semiconductor later able to reach an agreement regarding RPN? I seem to remember, about 1977-79, NS had a "Mathmetician" model that used RPN with a 3-level stack.

The quality of construction did not measure up to HP.

Re: Nat'l Semi & HP patents on RPN
Message #22 Posted by Jim Chumbley on 17 Nov 2003, 9:43 a.m.,
in response to message #21 by Karl Schneider

I'm sorry, Karl, but I don't know the answer to that question, although it bothered me at the time. If I remember correctly, the Mathematician was the only RPN machine NS ever produced, and there is a chance that it was withdrawn because of some back-channel, not-for-publication warning to National from Hewlett-Packard.

On the even darker side, we should remember that National Semiconductor was at that time an absolutely gigantic supplier of semiconductors, especially analog ones, and could well have been HP's largest supplier of semiconductors, although I'm not sure of this. In addition, National made quite a number of unique analog ICs, which may have been part of a number of HP's instrumentation products.

A real patent war would not have been good for either company.

Re: Nat'l Semi & HP patents on RPN
Message #23 Posted by Katie Wasserman on 17 Nov 2003, 1:50 p.m.,
in response to message #22 by Jim Chumbley

National Semiconductor (also manufactured under the name Novus) made several RPN calculators, not just the Mathematician. I've got 5 of them that use RPN:

3-level stack:
Mathematician PR (programmable)

4-level stack: 4640 Scientist Scientist PR (programmable)

Also, I think that the Novus 3500 was RPN too.

Re: Nat'l Semi & HP patents on RPN
Message #24 Posted by jimc on 17 Nov 2003, 2:05 p.m.,
in response to message #23 by Katie Wasserman

Thanks Katie!

I had a Novus Scientist (I think) that used RPN back in the late 79's (sheesh, I'm getting old). It was a HP-21 knock off. I don't remember too much about it, other than it KINDA looked like a 21, but had lousy tactile feedback with little rectangular rubber/plastic keys and chewed through batteries like nobody's business. (was it a 9 volt?) Anyways, I sold it to a business major for 50 bux. I think I paid 75 for it. I put the 50 dollars towards a 21.

Do you have a link to a picture of it?

Message #25 Posted by db(martinez,california) on 17 Nov 2003, 11:42 p.m.,
in response to message #24 by jimc

jimc; You'll find a few more pictures than you are looking for here including several Nat Semi/Novus RPNs:

It's a space that Mike Davis loans to me. I've got about five more that i'll get around to posting someday. Be sure to look at the Corvus 500. It out HP'd HP. Also; if you're interested - Katie has archived some of the manuals for the "other voices" of RPN (along with a lot of other 1970's models) on her site. - d

Edited: 18 Nov 2003, 12:11 a.m.

Re: Non HP RPN
Message #26 Posted by jimc on 18 Nov 2003, 9:23 a.m.,
in response to message #25 by db(martinez,california)

Thanks db!

After perusing the images, I discovered I actually had the Mathematician model, not the Scientist. Funny how your memory plays tricks on you, as I was sure it had more functions!

Fascinating reading.

Thanks again.


Re: Nat'l Semi 4510 "Mathematician"
Message #27 Posted by Paul Brogger on 17 Nov 2003, 2:12 p.m.,
in response to message #21 by Karl Schneider

Coincidentally, I found one of these at the thrift store last week -- working, MWOB (mint, without box) condition. It has a 3-level stack from the user perspective, without T, without automatic duplication of the Z value during stack drop, and without any "roll" function. I had tried one of these in '76, before giving in and buying my first HP (-21), and had discarded it long ago.

The stack is also utilized in "internal" calculations of logs, trig functions, etc., and as a result the manual is the most interesting part: it's got something like 7 of its 32 pages with diagrams devoted to explanations of whether & when to rely on maintenance of the Y & Z values after performing each of the higher mathematical operations. All in all, it illustrates in dramatic terms just how valuable are the extra design elements and internal registers of H-P's implementations.

And it still has the "Made in Hong Kong" label on the back, and, yes, feels even cheesier that the original TI-30 (if that's possible)! (I'm still wondering whether to "eBay" it . . . )

Re: what is your favorite (YOUR OWN) RPN program?
Message #28 Posted by Veli-Pekka Nousiainen on 16 Nov 2003, 8:37 a.m.,
in response to message #1 by bill platt

> a: what sorts of things we use our calculators for,

consulting new users, toying around, years ago computer science studies lists and queues simulation in the 48.

>b: why RPN is good (or why keystoke programming in >general)

HP-71B Is best, RPN is good. You see the intermediate answers aas well. ROL calcs with 'Algebraic' on stack give even more versatility.

>c: why BASIC and other methods are good

in a good BASIC (like th 71B) it easier to handle different types of files and records (fields witheen records) than using storage registers or lists of strings. The Commands can also be enhanced to take a different number of arguments. With Forth/Assembler and Saturn achitecture you get all the possible ways of calculating. The only thing missign might be the VisiCalc ROM from the 75C calculator. Now _that_ was a piece of gold.

> Be sure that you describe a program that *you yourself* > wrote--not something you got out of a book, or modified > from someone else. It *has* to be your very own thing.

71B & Foth/Assember: cracking the Secure bit for a desperate customer using a small ML program. The IDS where great and woth every grand.

49G I wrote the STARTEQW for a Custom to be used with the EQW, pure UserRPL

49G also an APPS enhancement that also added numbers to the custom list members (uses a message handler)

I can't recall my 25 and 41CV/CX programs anymore

wait-a-minute, on STaK pages there is still a number of our newsletter from 1992. There I introduce some new 48GX commands programmed in the 48S model to make the old model more compatible.

Then there are literally thousands of small routines and example which you could find with Google or dig out of the brains of the Finnish HP 48/49 users...:-D

There also a few commercial products for the 71B, 48GX, and 49G

Finally there is a small error message translation library FINLIB49, which can be founf here:

I surely have forgotten many nice routines Could it be something like this for the 41CV: ('=super T)

00 LBL'1-2-1

01 .02 @ line one of the code

02 %T @ line 2 of the code

03 END

# VPN #

Re: what is your favorite (YOUR OWN) RPN program?
Message #29 Posted by Gordon on 16 Nov 2003, 9:33 a.m.,
in response to message #1 by bill platt

Back in 1983 I used my 11C almost daily at work to calculate reliability predictions using Arhenius equation and to help with Weibull plots. The programs filled the memory and i wished I could afford a 15C !

Re: what is your favorite (YOUR OWN) RPN program?
Message #30 Posted by Ed Look on 16 Nov 2003, 6:42 p.m.,
in response to message #1 by bill platt


I am embarassed sometimes to post or even just read here (or comp.sys.hp48) because I used to be so proud of myself if I could make the simplest program work on my old 34C. I tended to try to automate the summing of data points, linear regression, pop out the slope and intercept and if I had to worry a bit about the shape or scatter of my "line", put in an extra step for the correlation coefficient. Later on, I just modified it to get max, min, and mean on a set of numbers. Not anything like what I read here, but boy it streamlines my life... a little bit, anyway. Well, there was that time I got it give me voltages from the Nernst equation, simpler job, and boy, that was a loooong time ago.


Re: what is your favorite (YOUR OWN) RPN program?
Message #31 Posted by karl gruber on 16 Nov 2003, 8:03 p.m.,
in response to message #30 by Ed Look

My favorite self written program ia one which calculates the weight and balance for a Beechcraft King Air 200.

It was actually approved by the FAA, for air taxi use.

Best, Karl HP-41 Hoarder

Re: what is your favorite (YOUR OWN) RPN program?
Message #32 Posted by Ben Salinas on 16 Nov 2003, 11:27 p.m.,
in response to message #1 by bill platt

Well, I have a few decent programs for my 32sii (none of the decent ones are typed up) For a long while I was on a game kick, so I programmed a number guessing game (where you guess a random number and it tells you if you are too high or too low), and I got into making stop animation (yes, on the 32sii... you are very limited on the types of characters, and it eats up a lot of memory because for each frame you have to enter an equation)

I also wrote a program, which probably is the most useful of all my programs, to do gas problems. It would do gas problems in torrs, mm Hg, and atmospheres. This was the first time I used flags. My other useful program was incredibley unuseful. I wrote a program that would calculate standard deviation. I know that that is a built in feature (now).

Finally, is my Tic Tac Toe program. I started programming it in December of last year, and have several different releases, all of which are unreleased. Basically, I will think of a more efficient way of programming it, and restart. I would always run out of memory before getting to the data entry part of the program, but now that I have discovered inderect referencing, it will be much easier. I should have enough room to even include AI.


OT re: Re: what is your favorite (YOUR OWN) RPN program?
Message #33 Posted by Ed Look on 17 Nov 2003, 12:13 a.m.,
in response to message #32 by Ben Salinas

This is what I mean! See, you programmed the various gas laws, hey, I'll even bet you saved "R" to ten or twelve digits in some register after you calculated it out for yourself since no entry level textbook gives it you for more than four or five digits, and probably played with various permutations of the form of the equations.

A "basic" (NOT LOW end) calculator like the 32SII is more suited to actually making a student familiarize himself with the equations unlike a more features-loaded model, like any company's graphing calcs, which tend to already prerecord such equations in their libraries. Of course, I'm sure even copies of keystroke programmed equations are available for photocopy or download somewhere, but even doing that forces the person to actually go through the program steps!

the importance of keystroke programming
Message #34 Posted by Ben Salinas on 17 Nov 2003, 9:15 a.m.,
in response to message #33 by Ed Look


Another example of this is when we were covering bases in digital electronics (a required course), and my teacher taught us how to convert bases, and would ask us questions about converting all bases, not just hex,decimal, octal, and binary, so I wrote a program that would convert any base into any other base. I asked my teacher if I could use it, and he said, "If you understand it well enough to write a program, then of course you can use it."

Another reason I like keystroke programming: It is quick to use -Ben

Re: the importance of keystroke programming
Message #35 Posted by r. d. bärtschiger. on 17 Nov 2003, 2:50 p.m.,
in response to message #34 by Ben Salinas

Have you perhaps seen the article on page 12 of HP Key Notes, Vol. 3 No. 2, May 1979 right column? There were a couple of corrections to this program which were listed in Vol. 3 No. 3 P. 10 & Vol. 4 No. 1 P. 2. Just thought you might be interested in how someone else did this to compare it with your own program.


Re: the importance of keystroke programming
Message #36 Posted by Ben Salinas on 17 Nov 2003, 6:31 p.m.,
in response to message #35 by r. d. bärtschiger.

No, I have not seen that. Is it some sort of base conversion program, or what? -ben

Re: the importance of keystroke programming
Message #37 Posted by r. d. bärtschiger. on 17 Nov 2003, 7:07 p.m.,
in response to message #36 by Ben Salinas

Yes, it is an all base number conversion program. Quoting from the program description as given by the author, Cass R. Lewart:

"Here is my program that converts an integer argument from any base to any base in only 49 steps. I saw a description of a similar program in the Users' Library (00409D) but it required 135 steps. I think that many KEY NOTES readers will be interested in this one."

The program listed was written for the HP-67.


My 15C program from the '80s
Message #38 Posted by Karl Schneider on 17 Nov 2003, 3:44 a.m.,
in response to message #1 by bill platt

In the mid-1980's, I maintained several Fortran 77 software programs that ran on Sperry-Univac mainframes. The software was written to provide large line-printer post-mortem memory dumps when execution failed for some reason.

Sperry utilized 36-bit words, with integers negated by ones-complement. Words of memory were listed as 12-digit octal strings. This practice differed from that of IBM (32-bit words) and CDC (60-bit words), which, I believe, also favored twos-complement.

Anyway, I got tired of manually deciphering 12-digit octal values in the PMD listings to find the value of a floating-point variable at the time of program termination. So, I wrote a program for my 15C to do so.

The program accepted the 12-digit octal values in two parts -- the 3-digit signed exponent followed by the 9-digit signed mantissa. It checked for any digit larger than 7, stopping with a blinking display if it found one. After a number of seconds, it calculated the correct floating-point decimal value of the encoded word.

Recently, I got a 16C, and see that I could have written a slicker program using its capabilities -- e.g., setting word size and octal mode, extracting bits. A program for the 16C would allow entry of the word as a single string, refusing to accept extra digits or anything other than 0-7. Also, the integer conversions were built in, which leads me to an interesting footnote:

Among RPN HP calculators, only the 16C, to my knowledge, has built-in processing of ones-complement signed integers in addition to unsigned and twos-complement. The Pioneers and RPL models support only twos-complement, and the HP-41 Advantage ROM supports only unsigned integers.

Re: what is your favorite (YOUR OWN) RPN program?
Message #39 Posted by on 17 Nov 2003, 4:28 a.m.,
in response to message #1 by bill platt

My favourite program was written for my 1st HP, a 11C. I managed to program the roots solution of y = ax² + bx + c without using any register (only the stack).

Not a big deal actually, but at that time I was 14 and I thought challenging and evidence of mastering the stack not to use any register.

This impressed the "TI clan" of my schoolmates (HP were 2 or 3 times more expensive than TI's at that time and only a few of us had the privilege of pesessing one) who found something "magic" on HP calculators to do so as such a challenge was just impossible to them.

Re: what is your favorite (YOUR OWN) RPN program?
Message #40 Posted by Ron Ross on 17 Nov 2003, 9:40 a.m.,
in response to message #1 by bill platt

Newton’s Law of Cooling My favorite program actually makes use of the solver in the 42s. I used this program often when I was an instrument tech for a chemical plant. I normally used it to determine how good of condition or well the heat exchangers were working and if they needed cleaning. Right after an exchanger was cleaned or worked on, I would check it out by using Newton’s Law of Cooling to find out its heating constant. Since this is a two stage problem the solver is better than a program for this type of application.

I would take temperature readings at 5 minutes, find the time constant and predict the time for 10 minutes out (to verify my time constant). Every couple of weeks I would recheck the time constant of the reactor and if it started to degrade or slow in its heating cycle, I knew the Heat exchanger was failing. This allowed the maintenance dept. a better cycle of repair than just a 6 month cycle, fix it whether it needed it or not (which is what was used before). Often the heat exchanger would degrade after 4 months but sometimes they might last 8-12 months, but maintenance did not want to fix what wasn’t broke. Documentation always made the crew feel better, knowing the system they were going to fix, needed fixing. I myself worked on these systems located in a pit a couple times. NO ONE wanted to fix a working heat exchanger!

The Solver allows for any temperature and/or time scale (just stay in the same units). It works great at predicting future temperatures or time constants. And the 42s allows long variable names, which is great for looking at this program years later and still knowing what each variable is for.


Here is the formula listed: (Ti-TA)e^(K x TIME) + TA = TF

Re: what is your favorite (YOUR OWN) RPN program?
Message #41 Posted by Jim Chumbley on 17 Nov 2003, 10:39 a.m.,
in response to message #1 by bill platt

May I mention one more RPN program, which is more in keeping with the spirit of the other entries than my NS program was?

In 1970, I had to analyze the time in decimal hours that operators spent exercizing various machines being subjected to reliability testing. This irksome task required the efforts of two technicians working full time.

I persuaded the company to buy an HP-9100A, with printer, plotter, and (the nowadays apparently forgotten accessory) a mark/sense card reader. The card reader read IBM punch-card sized cards that had been marked in pencil. The placement of the pencil marks could be interpreted by the 9100, and the engineer could define these to mean anything he wanted.

I wanted it to mean time. So I designed the cards and had them printed and introduced them to the operators, explaining how to convert time in h-m-s to binary-coded entries in pencil marks on each card. This was, shall we say, somewhat less successfully received than I had hoped. Not to worry! I backed off, had the operators write down in numbers the time information needed and asked their supervisors to convert to markings on the cards. We were amazed to find that they quickly learned to make the conversions from h-m-s to binary-coded entries in their heads and to finish the marking of the cards in 20-30 minutes.

They sent each day's cards to me (from all three shifts) and I zipped them through the mark/sense card reader. The 9100 completed the analysis with finished reports. All this on a tiny little 40-lb. machine the size of a Selectric typewriter with 196 programming steps, 16 registers, and 1 flag--Oh, how I needed just 1 more flag! It had only a 3-register non-automatic stack.

And lastly, the key that was so badly misnamed in later machines as "Enter" was simply labelled with an arrow pointing "Up." And this key, while double key length, was placed vertically rather than horizontally. Look at the numeric keypad on your PC's keyboard.

Even now when I write RPN programs for my 41CX I still write "Up" for this function. Think about it for a second, and you'll realize that those of us who raised such a howl in 1972 about the HP-35 having this key labelled "Enter" were right. Nothing is being "enter"ed. It is being raised "up" from the x-reg to the y-reg. Maybe the reason that it was not called "Up" on the HP-35 was because that key had to be horizontal to fit in the keyboard.

And to think that now we have good HP customers who mourn the lack on the 49g+ of a double-width, horizontal "Enter" key. Horse-feathers! Shame on you young whipper-snappers! I want a double-height, vertical "Up" key!

Thanks for letting me tell two stories.

Edited: 17 Nov 2003, 11:00 a.m.

favorite RPN program--Thanks!
Message #42 Posted by bill platt on 17 Nov 2003, 6:26 p.m.,
in response to message #1 by bill platt

This has been great fun! And I've learned a lot--many great stories (hopefully more on the way....some familiar names have not posted yet......) Last night we went to an excellent concert by "Andes Manta," a group from Ecuador who play amazing tunes on pan-pipes, charranga, bandolin, and all sorts of cool wooden, where is the rest of our South American contingent---how about some favorite programs from the other side of the Caribean?

Best regards,

Bill Platt

Edited: 17 Nov 2003, 6:31 p.m.

Re: favorite RPN program--Thanks!
Message #43 Posted by Nelson M. Sicuro (Brazil) on 17 Nov 2003, 7:22 p.m.,
in response to message #42 by bill platt

Ok, I was remembering one episode...

I was with my family on the beach, and we are playing a card game called "Truco". Normally the points are counted with a box of matches, but in that time we haven't any! I was with my brand new HP-42S (it was 1990 then) and I wrote a little program on the 42S, to sum our points...

I'm not a engineer nor mathematician, I'm a computer programmer and I learned to program on a HP-15C (and a small Sinclar ZX-81 compatible computer) back in 1983. That "Truco" program was not any fancy algorithm, but I used menus and the score was showing on screen for both teams - and wrote it "on the fly" in about 15 minutes, while waiting my turn to enter in the game...

They where impressed, and was very fun!

My 2¢... ;)


Re: what is your favorite (YOUR OWN) RPN program?
Message #44 Posted by Kraut on 17 Nov 2003, 8:12 p.m.,
in response to message #1 by bill platt

I have written a complete compressible flow function table solver, including classic 1D flow functions, normal shock tables, rayleigh flow and fanno flow functions.

It includes a "Preprocessor" that allows choosing between air, combustion products, steam (assumed to be an ideal gas in this case) and, subsequently, automatically selects the correct gas properties in the background.

It also allows entering a random gas via a molocular weight and specific heat ratio.

In the preprocessor, left shifting the gas selections initializes for metric units, a straight hit on the selection keys initialize for english units.

I have also included a method for "extracting" a desired expression for the chosen function, for easy subsitution to the stack in a format which makes using that chosen particular expression with the built-in equation solver easy. This allows for (fairly) seamless reverse use of the table, as well.

THAT one is my favorite.

Taking a close 2nd place is a similiar program that I wrote that calculates the ISA standard atmosphere given an altitude, then allows solving for the unknown air speed given one of the three following air speeds: true, corrected or calibrated air speed (in knots).

No, I'm not that bored, I really need these for my job.

With all of the computing available now relative to 15-20 years ago, there is still NO substitute to having such power in one (hand held) flexible package.

I go way back to the 67, the TI58 (ugh), then the 41s, then the 48s, and now the 49s. Love(d) programming ALL of them.

I'm showing my age a little bit...

Frank B

Re: what is your favorite (YOUR OWN) RPN program?
Message #45 Posted by Larry Corrado, USA (WI) on 17 Nov 2003, 10:54 p.m.,
in response to message #1 by bill platt

My favorite RPN calculator program was one I wrote in about 1977, for my HP-25. I was fascinated with the concept of random numbers, and the idea of computing (pseudo) random numbers. I found a simple algorithm that essentially kept cubing a real number and extracting the first digit in the tenths place as random. I was curious as to whether this could pass a simple frequency test. Thus, I wrote a 49-step program for my HP-25 that kept track of how many times each of the digits between 0 and 9 were generated in a test run.

One of the main problems I encountered was storing the 10 counters needed (one for each digit), with only 8 registers available. My solution, interesting for me, a novice programmer, was storing counts for three digits in one register by using the three lowest-order integer positions for one digit, the next three positions for the second digit, and the next three places for the third digit. I was thus able to keep count of all 10 digits in four registers, with a maximum of 999 for any one counter.

I recall leaving the machine running for hours at a time, testing tens of thousands of digits in the process. After a number of trial runs, I found that the digits appeared to be evenly distributed as expected.

Fond memories…

Regards to all. Larry

Re: what is your favorite (YOUR OWN) RPN program?
Message #46 Posted by David Brunell on 18 Nov 2003, 5:21 p.m.,
in response to message #1 by bill platt

If you will include RPL programs in your survey, then the one I am most proud of is my Smith Chart Companion, which I presented at the 1992 RF Expo (USA). From the abstract:

The Smith chart is a very useful tool for the analysis of transmission line problems as well as the design of high-frequency amplifiers. Its utility lies in the fact that the relationships between complex impedances and reflection coefficients are represented in an intuitive, graphical way. The price paid for this graphical technique is poor accuracy and interpolation headaches reminiscent of slide rule days. The Smith Chart Companion software has been designed to offload the computational tasks to a programmable calculator while maintaining the graphical ease of use inherent in the chart itself.

I'd be happy to send anyone interested a copy of the software.



Edited: 18 Nov 2003, 5:22 p.m.

From BASIC to RPL [long]
Message #47 Posted by Tizedes Csaba on 18 Nov 2003, 7:34 p.m.,
in response to message #1 by bill platt

Some of my favourite programs (all of it written by myself):


When I was young, I wrote a little BASIC program for my CASIO FX-850P. It was a molar-mass calculator. It had two vectors: M$() contained the symbols of elements (M$(1)="H",...), and M() contained atomic weights of elements, in same order.

When I typed the chemical formula, this program transferred that to a string, what was an evaluable formula to calculate molar-mass:

"CuSO4.5H2O" -> "M(29)+M(14)+M(8)*4+5*(M(1)*2+M(8))" then I used 'VALF()' function to evaluate it.


I wrote a tip calculator for my HP48SX. I never used it... :)


I wrote a Venus-calendar to my girlfriend. She's favourite planet is Venus, and she want to know, when and where it visible.

The orbits of Venus and Earth are good approximate with circles. This program use "linear" estimation of orbits, and calculates famous points of thats, and calculates the phase of Venus for any day. (It's not a really program, it's some of equations only...for my 48SX.)


I wrote a little program to calculate settle-velocity of gold-grains in the Duna (Duna is the largest river of Hungary) for HP32SII.


I wrote a partial derivative program for any variable for HP32SII. [I posted it to 'Program Library', but this site not freshed yet. It use statistical registers and 'i' to make calculations. All of other registers are free. This program calculates partial derivative numerically and works with SOLVER and with INTEGRATE.]


I wrote some equations to my mother, to optimize she's egg-incubator 'economically'. (What is the good egg? Chicken, duck, goose or maybe guinea fowl???)


In the University (some weeks ago) I wrote a little program, what maked some additional calculations of sterilyzing-time of tomato sauce. It uses idealized spherical preserving jar geometry, and used Fourier-series with four elements. When program ended, I transferred the result to my PC, and the presentation maked on it. OBSESSION :9


And finally a BASIC program for my CASIO: I wrote a program to calculate how many cucumbers we can to push to a preserving jar. It was important, because we had got some jars, and we don't know how many kilograms of cucumber we have need.

The program was not worked. We cutted little discs from paper, and drawed circles with some diameter like jars, and we try to put discs into the circles, then we calculated the approximated mass of cucumbers.

And many-many, what I liked... :)


Ps.: I wrote a little counter program for Z80 microprocessor in assembly, many-many years ago. It counts up to 255 digits on the screen. On my ENTERPRISE 128 (that was my first HOME COMPUTER!) it counted to 1e6 about 24 seconds. Hmm... That was wonderful...! :)

Re: what is your favorite (YOUR OWN) RPN program?
Message #48 Posted by James M. Prange on 19 Nov 2003, 8:53 p.m.,
in response to message #1 by bill platt

Actually a pair of RPL programs that have been on every calculator I've had since the 28S.

\<< 25.4 * \>>
\<< 25.4 / \>>


[ Return to Index | Top of Index ]

Go back to the main exhibit hall